P.S. My uncle didn't start speaking at all until he was 4-years-old. Now he won't shut up at all!
At three years old, typically, a child can speak 4 to 5 word sentences. It sounds like your child is speech delayed and would benefit from therapy. I would hold off on the diagnosis of ASD, however, because if your child doesn't have ASD, it will follow him/her and be difficult to get removed from their medical record if something else is in fact a problem. I also don't think school personnel should attempt to diagnose your child. That should be left up to your child's physician or neurologist. There is a whole gammit of exams your child would need to go through for an accurate ASD dianosis. It may very well be a hearing problem or something else that is delaying speech. Typically, a child who communicates without difficulty using eye contact and verbal cues and pointing, doesn't have ASD. I'd leave it up to the professionals to diagnose. Just my opinion.
It's kinda hard to determine from what you wrote. For me, the first part sounds like my son who has Asperger's, a mild form of autism. He too was a late talker...putting two words together by 3, yet he could copy the ABC song or "that's elmo's world" song. The rest sound a lot like my daughter, minus the hand flaping and humming (my son hums). I am still trying to figure out her issues. So far we only have a speech delay, but I think she has sensory issues as well. She is almost 6 and has been in speech therapy since she was 4, but she did talk a lot earlier than my son. Stringing two words together a whole year before him. No one could understand her and her grammar was horrible. Her speech has improved tremendously! But we still need therapy. Both my kids have great eye contact, btw...so if they tell you your son has good eye contact, nothing wrong with him as far as autism spectrum disorders go, I would get a second opinion right away! I have heard so many moms who were brushed off because their kids had eye contact. All spectrum kids are so, so different.
I would say go along with the speech therapy and keep a close watch over your son. Do your research. Maybe he has mild autism/Asperger's and a lot of times they will get their diagnosis by the 3rd grade when they start to really stand out from the other kids. This is when my son was diagnosed. This is a late diagnosis, if you are concerned already at this age, push it! Get a 2nd opinion, but do your research. I have heard developmental pediatricians is the way to go, or anyone who is very familiar with diagnosing autism spectrum disorders. We have autism centers here who do the whole evaluations and diagnosing. We were so lucky to run into a great "team" through the school who evaluated him (which took most the year, unfortunately) and diagnosed him with autism spectrum disorder. We then took him to his ped who sent us to a neurologist who agreed with the school diagnosis, but then evaluated him with ADD as well, which a lot of times go hand in hand with spectrum disorders. With therapies through the school, he has done excellent and is an honor roll student.
Good luck in finding answers and go with your gut feeling.
Thank you for sharing your concerns. From what you wrote, I would agree with you. He has some things that a child with autism at that age would not be doing. It is your choice as to the direction you take in getting an evaluation. Consider the speech therapy and see where that goes.
If in the end, he does end up being on the Autism spectrum, it isn't the end of his life :-) Those on the spectrum are just as unique and we learn all sorts of things from them. Our eyes are opened to see things in new ways.
Things can change at this age as children don't develop at the same rate. Getting help with the problems he is now dealing with will help him and you. Having him monitored for changes is a good idea so you would know what direction to go as he gets older.
Please keep us updated. Each day is precious with our little ones :-))