Since the Air Force would be signing you on in order for you to be a physician, you don't have to take any of the tests. The purpose of the ASVAB is to assess your strengths and assign you a job. If you get accepted to medical school, you've already proven that you can pass the testing requirements to become a physician, so they don't have to reassess what position you should have in the Air Force.
At this point, focus on getting in to medical school. If you're dead set on HPSP (you should read the stickies on here) then about the same time you start applying to medical school, go ahead and contact the Medical recruiter for the AF. (Not the regular recruiter, the Medical branch recruiter.) You can start the paperwork then. It took me about 4 months to go from contact to Oath of Office signed, and it was a hassle, so I wouldn't put it off until the last second.
Good luck man. BOHICA.