Hiya!
I would suggest that you see the counselor first. Counselors are the professionals that will talk to you [at length] about your personal issues. Medical doctors will just check for biological causes of your phobia. Medical doctors also can prescribe medicine for the phobia. I would go to the counselor first because if you go to the doctor they will run some tests on you and then tell you to go to the counselor anyway. Atleast from what you said, the doctor is busy for many weeks ahead. So just make an appointment with a counselor now. I guess later on you can get a physical with the doctor to rule out physical causes of anxiety.
Also, I would contact your insurance just to make sure that you are covered for mental health issues. It is also important to ask which psychologist/counselors are in their network. In-network psychologists/counselor will have more coverage than out-of-network psychologist/counselors. Your insurance company should have a list of providers (psychologist/counselors) in your area.
Finally, let me suggest that you arrange an appointment with a counselor that is proficient in Cognitive Behavioral Therapy or Rational Emotive Therapy. In the psychological literature, these types of therapies have a large amount of empirical evidence to support their effectiveness across a wide range of psychological problems (i.e., OCD, social phobia, other general phobias, etc.) This is my preferrence because I believe that it helped me a lot.
Well, Good Luck!
-ORL