I am so sorry!!
I have had severe allergies (allergic to everything including my own bladder!) since I was two. My daughter is the same way!
First and foremost, get him allergy tested. Find a well-respected pediatric allergist in your area. Ask local pediatricians, mothers what their recommendations are.
Your son could be having allergic rxn to your laundry detergent, dryer sheet, soap, food allergies, pollen count, mold count in your house, et al. It could literally be ANYTHING. In addition, he could be one of the lucky ppl (like my family) who are not only allergic to alot of things, but also born with an overabundance of histamine making him allergic to his own body resulting in allergic rxn when there is no noticeable allergen.
My allergist just recently told me they've discovered (not theory, fact) that one is born with allergies imprinted on DNA, but they have a protein coating. When those protein coatings are dissolved due to things such as environmental changes, stress, illness, etc, "new" allergies appear and sometimes they seem to disappear or "grow out" of them.
Do NOT put your son on and off steriods. It's dangerous. I was on/off steriods my entire life. There are very noticeable and life-impacting complications from prednisone use longterm.
Allergy shots are experimental. They don't know why it works for some people, doesn't work for others, and makes others collapse in fits of asphyxia.
Get to a pediatric allergist immediately. Use Benadryl in the meantime.