Were it an allergic reaction, however, it could be an allergic response to certain classes of antibiotics;
for example
Biaxin and Zithromax are in a class of drugs called Macrolides so that, if allergic, you might be allergic to all antibiotics in that Class. That the 4 antibiotics you mention represent 3 different classes of antibiotics, it would also be unlikely for you to become allergic to three different classes of antibiotics, pretty much at the same time.