He may need antibiotics, but some ASD kids can't take them, or the dose needs to be way different.
Gargling with soluble asprin can help, but I couldn't see how old he is, and you have to be careful with that too.
Even gargling with slightly salty water can help.
A second dentist seconded what the first said. Lots of children do not notice that the roots of the babyteeth are degenorating. Some do and can get abcesses. Usually the body gets rid of the filth without interference from dentists, docters or medication. She started with these abcesses around the age of 7. But she's not a quick changer of teeth. And the biggest abcesses she had on places where the molar is still in her mouth.
I hope what's happening to your son is something as innocent as was the case with my daughter.
Good luck at the dentist this afternoon.
Also, some people are just hyposensitive to pain, or have sensitivities to some pain but not to others which can lead to uneven responses or disproportionate responses to pain.
It is probably worth monitoring this in order to avoid a situation where something serious occurs but your son has no pain to indicate this - but it sounds like you are already doing this.
Regarding the risk of infection - are there any prescription mouthwashes that can help? I used one when I had problems with my wisdom teeth in order to prevent infection but that one was not suitable for children. (it also caused staining of my teeth, a common side effect, but my dentist was able to clean the stains off easily).
Slightly salted water is allready doing a lot of good. Soothing and cleaning. But its a weird 'luke' tast.

That makes sense. My son is 6 and his baby teeth were quite late coming in so the dentist reckoned a while back that his adult teeth probably wouldn't come in until he was 7 or older. Hopefully, he does have the same issue as your daughter, but they do look pretty alarming. It's very difficult to get my son to look in his mouth, but because these abcesses are right at the front under his top lip, I can see them when he speaks or smiles.
Although he doesn't seem to be in pain, he's had a couple of really major tantrums over the past day or two, which is out of character - even for him! - and I wondered if that was maybe his way of expressing the pain.
I'm also really worried about the risk of infection and his mouth becoming a real mess.
The tantrums could be related to other things too of course. Like knowing you have to go and see the dentist. Or knowing there might be something wrong with your mouth and who knows what they'll find. But it could be pain.
I hope the two of you will be fine this afternoon.
I hope the medication will do something good. And the pulling of the teeth as well.
Good luck.
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Our children (at least the ones on the spectrum) are just the same. So is Natalie, at least according to the first part of her post ...
... that reminds me of the incident when our daughter put her foot into a bicycle's front wheel. Result: broken ankle. Question: Did it hurt? Answer: Yes, because I could see the bones.
I've read that children on the spectrum are in danger from Appendicitis (e.g.) because they (at least some of them) will not indicate that they are in pain.
Sometimes you are so like my husband. Have you tried cloves yet to ease the pain?
He does go to the dentist now. But that's a dentist who has special talents adressing scared patients.
My dad pulled lot's of teeth himself, not wanting the sedative. Not afraid of the pain but really scared of the sedation.
I'm afraid of sedation too.
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*warning - I mean it!*
I have odd reactions to pain. Either oversensitive or under. Currently I have one half of a left tooth missing and a rather large dint in a back one. I'm scared of the dentist and I keep thinking that if they gas me or inject me I'm gonna die, so I've had intermittant pain for the last year and a half. It's there now. I clean with an interseminal toothbrush and stick sensodyne on it. When it's really bad I take pain killers. I know I should get it sorted out but I'm really scared of going to the dentist. They bang around in my mouth and then get all indignant when I'm retching. I'm always working not to retch when I clean my teeth in the morning.
Yee ouch! Nasty one, but no easy solution to that kind of problem. Have you tried asking for recommendations for a dentist who's really good with people who're terrified? Some dentists use hypnotism instead of gas or injections - do you think that would be helpful at all?
I'm really impressed with our dentist, because he's taking things as slowly as he can, not just in dealing with this current problem, but because he doesn't want my son to have a negative experience which will affect him in the future.
Today, he decided pretty quickly that it wasn't going to work, so although it was pretty traumatic at the time, it wasn't long drawn out.
I'm in Spain, and not too clever with the language yet. I'd like to use hypnotism and I think I'm probably highly suggestible but because I know about the dynamics of hypnotism and have certain barriers of my own put up against outside suggestion (years of meditation and magick), then I don't think it would work.
I definately need a dentist like yours that understands when enough is enough.
There are dentists who can treat you without hypnosis and without sedation. Some are good in explaining what they do and in listening to what you have to say. My favorite dentist did rootcanal treatment without sedation. He know's I can stand pain very well. He also knows that I feel things others cannot feel. And he has learned to react on them.
There are also dentists who use accupuncture. That would be a way of avoiding hypnosis and syringes too.
But is is a big advantage if you can understand a dentist. Because when enough is enough he/she should understand what you are saying.
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When I read your post despite the warning, I remembered that my wife has to see the dentist because of similar problems and she hasn't been there for several years. 
My turn.. Don't want to. But cannot ignore it.
Toothache. I did feel something was not right. But it was not really hurting yet. But now I really cannot ignore it. Since a few years my whole face nerve will hurt if something is wrong with a tooth.
Luckily not all the time. But it comes and goes in horrible waves. So half of my face is aching. Lower jaw, upper jaw, towards my eye. And it just stops in the middle of my face.
Today it is not that bad. It just hurts like hell for half an hour and then it's gone again. Just a dull feeling left. Not yet the sensation that the left part of my face is burned or so. And it is not constant. I don't want it that bad ever again.
The last years a visit to the dentist, the physiotherapist, and painkillers together worked.
I've got a dentist appointment in 19 days. But hope I can get to him sooner. Hope it's my own dentist because photo's do not show inflamations in my jaw and he is aware of that. This does feel like a root-canal-treatment is needed.
My physiotherapist is on a holiday.
But there is ibuprofen, and it does help today (did not do a thing last time). And there is paracetamol.
At the moment my head is just dull and feels bruised but not painful. Otherwise I would not be here at my keyboard.
Anyone familiar with this face-ache?
So now the pain is reasonable, but half of my lips hurt.
I'm on paracetamol with codeine now. Hope to stand it till monday so I can go and see my own dentist. Otherwise it will be a strange dentist. And it will be difficult explaining that I'm not even sure what molar is doing it. There are two candidates. But every teeth on the left is sore now. So who am I to choose. And mostly X-rays don't tell with me. My own dentist does know about this and he knows I can't stand regular local aneastetics.
That's not daft, it's a good idea because this dentist might know better how to interpret your reactions according to your cultural background. You might avoid some misunderstandings. Good luck!