Yes. Absolutely. A problem can be an interface of both the physical and the psychological. I do encourage you to talk to your doctor. One way to approach it might be to share your letter. You do want to be sure that all medical reasons for the problem have been checked.
If so, then I do urge you to see a psychologist. It is very possible that you lost your “voice”, i.e., your ability to express yourself, for psychological reasons. You have listed plenty of reasons why you might, however unconsciously, want to maintain your silence.
Please don’t be embarrassed by this. If the root of the problem is psychological, it is probably in some way self-protective. You and your therapist will figure it out. With good support and practical help, I have every reason to believe you’ll regain the power of your own speech.
I wish you well,