I'm not sure how it goes with adults, but with my child most of the process is several people answering questions about your child. Your doctor is not going to figure out if you have AS unless you give them information first. For you being an adult, printing off a list of AS traits that you feel pertain to you is starting the process that will happen anyway. Your psychiatrist may not value online tests, but that doesn't mean that they can't give a person information and insight. Just don't say you think you have autism because of your score, talk about why the score came out that way and what that may mean. Take your list of things worth mentioning, write down the things you experience that make you think that you have AS, talk about the tests and go from there. Maybe you and your boyfriend can explore this possibility together, just for the sake of doing it for your own piece of mind. Go over things, research traits and do tests and then talk about it together. He may see what his mother doesn't and get on board with you before you present this to your doctor. Then he may be more supportive and this won't be so hard for you because you won't be alone.
I'm sure there is a big difference between the kids your boyfriends mother see's and what manifests in adults. This may be something you and your boyfriend can explore. Autism is a spectrum, and there are spectrums in each trait in each person, and each person grows in different ways in different areas at different rates. My son has perfect, natural eye contact, that doesn't mean he doesn't have autism, he does. I'm sure of it. I've had people say he doesn't JUST because of that. 