Hello and welcome to Just Answer. I can tell from your letter how much you care about your son and want to help him. Unfortunately, there is no single test which can diagnose ADHD. The diagnosis is based on observation of behavioral characteristics.
I've provided a link (below) here to an excellent discussion on the Mayo Clinic website. Among other things, it lists the diagnostic criteria for ADHD. If you carefully document the behaviors you observe and then discuss your observations with your pediatrician or family doctor, you should be able to partner with them in creating a plan to help your child. If your pediatrician or family doctor isn't open to such a discussion, you could start over with a new provider, or perhaps seek an opinion from a psychologist or neurologist. Here is the Mayo Clinic article:
I hope this guidance is helpful and I send you my sincere best wishes,