Should I try Winter Track?

I am a Sophomore at a private high school with about 400 total kids in it. I have never been a great or even good runner, with a mile time of about 12-14 minutes in middle school. However, I have never trained for or been serious about running. I weigh a little under 150 pounds at the moment, but I have lost 17 pounds in the past month. Also, I have a touch of arthritis in my feet, but I won't let that stop me from doing what I want. I play golf in the fall, and I am thinking of playing tennis in the spring. But I do not have a winter sport. I was talking to my friend who runs cross country and track, and she recommended winter track. I have been thinking it was a good idea, but I was wondering if I should really do it. The only things I worry about are if running will be too much for me and if I can keep my grades up. My grades aren't perfect like they usually are, but my GPA is still a 3.6. So should I try winter track? Why or why not? Are there any other things I should know? Thanks