I'm not a doctor, but I would say that the chances of getting pregnant while on your period is EXTREMELY slim, if not impossible. You need to ovulate, and the egg needs to be fertilized at the time of ovulation in order to be pregnant, and I don't think that's possible while your uterus is shedding all of it's lining (which is what your period is). Somebody correct me if I'm wrong!
As far as getting pregnant after you get off the shot, unless you have regular period to track your cycle, you wouldn't know when you're ovulating (even with a period, you don't know for sure without rigorously tracking your cycle), which means you won't know when an egg can be fertilized and implant. So, that could essensially happen at any time after you stop the shot.
If you're not up to date with your birth control, there's a risk of pregnancy, even if you haven't had a period yet.