If you are of age, then you are allowed to use the insurance without her having to approve it. You might need to check and be sure there is coverage for mental health, as that might be one reason she is dissuading you.
You have a doctor prescribing, and if your MD will continue, you won't need the psychiatrist for the time being (and as long as the meds work, and your MD agrees.)
Why not call some of the therapists that your insurance will cover, and verify that with them, and see if you even like their voice etc, on the phone?
I think it is a great thing that you are reaching out for help! Perhaps your mom feels she is part of your problem and thus can't handle you "finding" that out? It's tougher when parents don't support you, but once you have a good therapeutic relationship with a T, you'll get passed that.
I doubt any T worth his salt would say that to you. Ts help people become comfortable with themselves... whatever the reason they aren't (and thus seek counseling.) Ts help you learn how to change what you can and want to , and how to adapt to what you need to.
Go for it!