They prescribed the steroid because you clearly had a severe reaction to the antibiotic. If you had a true ANAPHYLACTIC reaction, acute response to the medication, it would have been a dire emergency treatment to save your life. Sounds like you were close to having nearly that severe. Benadryl is an anti-histamine to reduce the itching and aggravation as well as inflammation, but the steroid is stronger in sense of reducing inflammation and swelling. They are often given together to counteract and prevent worse problems of that nature.
Steroids are generally safe for short term things like this. Like any drug, there are some people who can't take steroids and can have allergies to them, however, they are used for treatment of allergic reactions.
Short term steroids should not cause lasting harmful effects, I call it the "good drug--bad drug". Excellent for short term use, can cause problems with long term use.
Long term use is often necessary for chronic lung problems, like COPD to help breathing, used long term in arthritic conditions, and some cancer treatments and transplants. Long term use can cause some bone loss like osteoporosis, thinning of skin, moon face, tissue and organ damage, but life saving.
Steroids are used in epidural blocks to reduce inflammation and relieve pain with nerve compression, can be injected into joints to reduce pain and inflammation.
In your case with the symptoms you had, they should be quite beneficial, and as much as I don't like medication myself, I would use it and not be afraid of any lasting effects of the steroid.
Be sure that you note in your history for future reference that you are ALLERGIC to the Z pack (Zithromax). You will be allergic to other drugs in that same classification, like Erythromycin, (E.E.S, E-Mycin, Ery-Tab)Biaxin.
Hope you feel better soon!