This answers all of your HIV questions, and if you can think of any more just reread about the 3. You had zero risk therefore testing is irrelevant to your situation because you had zero risk. HIV is a fragile virus, which is instantly inactivated in air and also in saliva which means it is effectively dead so it can't infect from touching, external rubbing or oral activities. It doesn't matter if you and they were actively bleeding or had cuts at the time either because the HIV is effectively dead.
Only 3 adult risks are the following:
1. unprotected penetrating vaginal with a penis. Only the head needs to be covered, so if that happened it is protected and there is zero risk
2. unprotected penetrating anal sex with a penis. Only the head needs to be covered, so if that happened it is protected and there is zero risk.
3. sharing hollow needles that you inject with.
The only way to get HIV is if you did one of the 3. The situation you describe is a long way from any of these 3.
Even with blood, lactation, cuts, rashes, burns, etc the air or the saliva does not allow inactivated virus to infect from touching, external rubbing or oral activities. This HIV science is 40 years old and very well established, so no detail that you can add to your encounter will change it from zero risk. Because of all the research statistics, doctors have calculated the risk from what you describe to be less than that of being hit by a meteor, therefore no one will get HIV from what you did in the next 40 years of your life either.
If you didn't have one of the 3 then you are just worrying about your own hiv theory - which is unrealistic for you to think that can become reality - so you should move on back to your happy life instead.
Don't bother calling the pediatrician about hiv because it is impossible for him to have it. But if he is still sick with that temperature then you might need to get him to a doctor.
Injesting infected fluid is not a risk for your 3 year old child. Saliva contains proteins that inhibits the virus.
You have been around for a long time, you should know that you have an HIV phobia. It wouldn't be a bad idea to seek counseling to get rid of this fear.