Repetitive behavior is definitely one of many signs of Autism. As is poor communication skills. You don't say if this is a new thing or if it has been going on for a while.
What happens when you tell him to not lick or not put his hands in his armpits? Does he cooperate or does he get agitated or annoyed? The behavior you're describing may be his version of stimming or self stimulatory behavior. Pay careful attention to when he does it and you might find triggers- loud noise, bright lights, smells, overly tired, etc. It could be anything. Talk to his teacher. Does he do this at school? Has the teacher noticed anything?
I've known one autistic boy who liked to lick things- something about the texture on his tongue. This same boy hated all kinds of bread because he couldn't stand it's texture.
In addition to having your Pediatrician research, go to your son's school and ask what you need to do to have him evaluated. Usually it begins with you writing a brief letter to the principal requesting the evaluation.
Best of luck to you.