First off- make *sure* you get all the debris out of it. Debris is just about *guaranteed* to contribute to infection.

2nd- use a triple antibiotic like neosporin. These things love to get gooey and infected.

3rd- you're doing a good thing by wrapping it- keeping it moist (with the natural lymph secretions and antibiotic) will help reduce scarring.

I think as long as it's not on a knee or joint or some such, you should be fine to exercise... but I'm not a doctor.