Sports medicine is a component of a physiotherapy degree. So if you do physiotheray you can go on to work in sports medicine. Especially if you study in Australia where sports medicine is an important part of the undergraduate program. Not all countries are like this however.

If you study sports medicine as sports science then you would working in that field and could not be open to all the great opportunities of the physio profession.

Sports Medicine is also a speciality that a doctor (medical degree) might do. These people of course work with sports physiotherapists and sports scientists as part of a team approach to client care. However studying medicine is another issue all together.

Hope this helps.