I started out as a case manager/social worker, and took some post grad psychology courses before deciding on medical school instead. I was not a math and science guy in school. Before that I had earned a graduate degree in education and worked in public high schools.
One thing you should be aware of if you decide on med school is that you would be trained as a physician first and foremost, and will always be a physician, who is specializing in Psychiatry. It will change who you are. I am a Physician, all the time now, it is how I see the world now to a large degree. This is good and bad. No longer a layman, many things are medicalized, including mental illness. I'm less laid back. I became much more disciplined, and much more of a perfectionist. This is also good and bad. Medical training tries to turn you into an ascetic workaholic, and it will succeed to some degree if you are to survive training and become a competent physician. Medical school, and then residency, is in my opinion, far more grueling than anything else I've ever done. It is financially more rewarding. I'm not sure if it is emotionally more rewarding. On the one hand I like having more responsibility and say in treatment planning, on the other hand it is also more frought with concerns that I could be sued for malpractice, etc. I'd still do it all again. Why? Why do people climb Mt. Everest?