Sulfameth/TMP and Prednisone together.?

My son was taking Sulfameth/TMP and prednisone together. Three days after taking his last dose of prednisone, he broke out in hives. I'm guessing a reaction to the Sulfameth. Why did it take him 10 days to have a reaction? Was the Prednisone keeping it under control and after the prednisone was got the hives showed up? After taking the Sulfameth for 10 days, how long may it take to get it out of his system. Liquid benadryl is not doing much for him.