learningman,
You could actually apply for assistantship in any US Universities. It would not cost you a dime and you would get a monthly paycheck by working for the professor. As good as it may sound, the competition is tough. You need to have a good GRE score and outstanding recommendation letters to begin with. I believe most of biomedical departments in US colleges are funded one way or the other.
I am not so familiar with biomedical, but I guess you have to invest huge amount of time and effort. Ph.D, despite its glory, can be hell. It can be a lonely path especially when you are working on your dissertation, alone, in a dark corner of a lab. And not to mention you have to do postdoc for three or more years for slave wages before landing on a tenure track position, if you are lucky. That said, you should not pay out of your pocket. Get a fellowship and/or an assistantship.
Before you begin this journey, you have to mentally prepare for the hardship, not finincially, but academically. Your advisor can drive you nuts and expect a lot from you. During the "dog days" of graduate school, you need some unrelenting passion to pull it off. Don't get me wrong. I believe you have what it takes to succeed.
Tough as it is, it could be very rewarding at the end.
Good luck!