A PT program will be MUCH easier to get into than a medical school. While not easy, a PT program will also be less academically challenging than medicine.
As a physical therapist, you will carry out and probably assign the treatment itself. As a physician, you will most likely just write the prescription to the PT and go with what they want to do. If you can work for a sports team, you may end up doing everything by yourself. While Sports Physical Therapy does not exist in medicine, there are sports medicine fellowships through a few fields. Medicine pay will be higher than physical therapy.
I know very little about PT admissions and they're probably about the same, but for medical school, assuming your grades are average or above, you will have to dedicate a few months to studying for MCAT and make at least a 30. Then spend another year waiting. For example, since this is March, and you study for the MCAT and take it by May at the latest, you can submit your application by June or July and then secondary applications from the school and then wait for interview for admission to class of 2013.
MO also has the first DO college, so that program is going to be very strong there. I would go to an MD school if I get in simply so that you have more choice come residency selection time, but then you won't get the OMM. To be fair, the only DO I have heard of practicing OMM after school was one of the admission officers at a DO school.
The thing about medicine is, there are so many options once you do go in, you may not want to do anything to do with physical therapy or sports medicine when you come out. It's also a very long road and a roundabout way of doing what you want to do when physical therapy may be a better route for you.
Additionally, DPT is going to be 3 years. Medicine will be 7 at the minimum, longer if you do fellowships or a longer residency. But you're pretty young, so this time difference may not ultimately mean much.