I have to take prednisone from time to time for a chronic medical condition and wouldn't recommend strenous exercise while you are taking it as it supresses your immune system. It's a powerful drug especially combined with an antibiotic. You must have a really bad allergy! I think you should err on the side of caution while you are immuno-suppressed.

I'm not medically qualified this is just based on personal experience. A pharmicist would be able to advise you. In the UK we can call any pharmicist and ask for advice - not sure how it works over there.

Hope you feel better soon - the blessing of prednisone is it should kick in quite quickly.