Have you noticed any difference after giving your son this medicine?
There is no one cure all drug for the autism itself.. just to treat certain aspects of the disorder... whatever might affect your son the most, if he seems to have a problem with implusivity and focus, then maybe this is why the doctor prescribed it. I have two daugthers with ADHD (one might actually be Asperger's) and this medicine seems to help them. There are many medications out there to treat the ADHD-like symptoms.
I recommend you find out everything you can about your son's autism, join groups for support - online and locally. And get him therapy.. there are many aspects of his disorder that will need to be dealt with, he may need phsycial therapy, occupational therapy, speech therapy and there are a host of other things that can be done for him. They key is early intervention and to get a head start to deal with each facet of how his autism affects him. Counseling and group therapy - for the whole family - may be in order as well. Some kids even go on anti-depressants... but my tendency is to think that since your child is so young, you've got a head start to avoid the magnitude of low self-esteem that comes with having this disorder, many of these kids know they are different and it leads to depression because of their lack of verbal skills/pragmatics, they can't express it quite right.
And if you are also feeling hesitant about medicine, Seek another professional's opinion. Adderall can cause a decrease in appetite and the doctor should watch him quite closely.. now is not the time for him to be losing weight, some doctors will recommend meal supplement shakes. If your son is a typical 3 year old he is probably a picky eater.. so him not having an appetite due to the medicine is going to make getting him to eat even harder.
I highly recommend getting "The Out-of-Sync Child" and the companion book "The Out-of-Sync Child Has Fun" book - it is an easy read and you will get your own ideas on how to deal with sensory issues your son may deal with. Many ideas for calming - aromatherapy, joint compression, gentle massages - all of these have worked for my 4 year old son.
You have a big challenge set before you, but there is lots of help and support out there, there are many options for services out there, privately and through the school district, that are available to help your son adjust and to gain the skills he needs to go to school and fit in as best as he is able. You are very blessed to recognize his challenges NOW so you can get a head start on helping him. Call your local school district to see what programs he may qualify for. Where I live they have an Early Intervention Program for 3-5 year olds, you'll have to have him evaluated with them to qualify, bring all your doctor's paperwork, he may qualify for special preschool programs in the school for kids like him. Check out and ask everywhere what is available.