I'm essentially saying you won't be able to do it as a Coast Guard officer. I'm sure people have started a second life, after getting out, and going back to school for an M.D. I don't know of any though.
I guess, you COULD be an M.D. and be in the Coast Guard reserves, but the two wouldn't be directly related.
As far as becoming a PHS doc working for the Coast Guard, they aren't the easiest billets to get. But remember, the Public Health Service is not the Coast Guard. The PHS docs assigned to the Coast Guard will wear Coast Guard uniforms (with a few differences), but they are not USCG officers. The FDA, CDC, IHS and BOP also use USPHS officers...