Testing for autism

I have a 4 year old little boy that I'm suspect may have some form of autism but am not sure.  He gets tongue tied when trying to explain what he wants or needs and gets very upset if you don't understand exactly what he means.  He is and always has been a tippy toe walker (he is my third child and is quite different from the other two at this age). He will throw temper tantrums particularly when his schedule is thrown off that are quiet violent. He is very independent and has "jobs" he has given himself around the house and will get again violent or quite stressed if his jobs are taken away or if somebody else does them. He is helping me put together a 500 piece...yes you read that right, puzzle and is very good at them.  He outgrew preschool puzzles awhile ago. He doesn't do the flapping and is social with other kids but also will occationally sit and rock like an autie. He likes everything in order to the point that when we went for his kindergarden assessment he had to reorganize their toys as they had dinosaurs with farm animals and he sat down and separated them all. If someone messes up a rug he will go "fix" it and likes the shoes in order by the door amongst other things.  If he needs something high he will stack chairs or milk crates in liu of asking someone taller. Do I ask his doctor at his well child check up to test him?

[laidoffmom]

I forgot to add he also can't stand tags in his clothes and is sensitive to certain materials