How would I find out which antibiotics I am allergic to?

Months ago when I had bronchitis, I was put on several antibiotics: Prednisone, Hydrocodone, and another one I can't recall. The Hydrocodone made me sleep really heavily and the second time I took it, it made me slightly nauseous. The next morning, I woke up covered in hives on nearly every part of my body. So I switched over to different antibiotics, save for the Prednisone, which I had to finish off bcuz A. I had been told to take them all till they were gone, and B. Bcuz I didn't react as much to them, which made their benefit outweigh the risks. I was able to deduce that I was allergic (very slightly) to Prednisone bcuz little bumps would appear on my hands when I took them. I could usually stop them from developing further by taking some 'Dryl. So after all that brouhaha was over and done with, I made a list of all the medicines I reacted to, and I keep it in my purse. The question is, how do I found out which of the medicines I actually have an allergy to, w/out putting my health at risk?