What can I do if my 16 yo son has been recently diagnosed with autism and is denying he has any problems, what should I do?

See a psychologist. See a psychologist as this requires professional assistance.
Get help. See a mental health professional. Why continue to suffer with whatever symptoms he is having when there is some relief to be had with the right help.
A core deficit in. Autism is lack of theory of mind, the inabilty to understand that, not why, someone can have a different point of view, the same reason he thinks you & all his teachers are wrong when you propose non-preferred tasks. He needs a therapist with expertise in autism. You can also give him books by dr. Temple grandin. She answers emails from people with autism through her publisher, future horizons.