During a sports activity I fell on an outstretched arm and felt instant pain, but not too severe. The next day I got x-rays which showed a torus fracture of the distal radius. I was put in a cast and still currently am and will be for 4 weeks. The doctor said it would be wise not to return to sports, but it is my last year before high school, and I really want to play. Is there any possibility I'll be able to return to sports?
You should never ask for medical advise in such an electronic medium, especially when you have already gotten an advise from a professional. Even if there are/were doctors or physiotherapists here, they would not (and should not) give any advise without having examined you in person.
You really should talk to a physio if you are serious about getting back on track with your training, and come up with a proper training plan. Keep in mind that early come-backs are among the most common reasons for serious injuries.
Serious injures have to be taken seriously specially when a professional told you this. I would like to encourage you to do a serious rehabilitation and after that re-evaluate the situation.
I understand your feeling as a quit from basketball a couple of years ago for a similar reason. It is frustrating when you really enjoy a specific sport and you have to quit, but your health is a priority.