Possibility of new allergy developing

Has he been using a lot of sunscreen? Sunscreen really irritates my son's ecxema to the point of what you are describing. We had to switch to using Cetaphil dermacontrol lotion that has SPF 30. Even Aveeno was a problem for him.

My grandson had the same problem. My daughter switched him to rice milk and the excema cleared up.

Part of the reason that sunblock irritates is that is does not allow the skin to breath. My daughters excema was always worse in the summer even without sunblock.
The only thing we found that did the trick was Desitine. I know it sounds crazy but zink is great for healing. She is 17 now and she still has a tube in her bathroom and uses it any time she gets a flare up. She puts it on before bed and by morning all gone. We put it on her anywhere she broke out. The trick is to put it on thin not always easy. The at night thing was she was less likely to rub it. Before I tried that her face would bleed and she would scratch at it so much. Same issue could only use the steroids and it would clear up but the min. we stoped back it would come so we knew we needed something we could use all the time to prevent. Once we got it under control we just applied the Desitine at even just the slightest sign of it and we never had another bleeding face or arms or legs or anything. Thankfully her face shows no signs of ever having been so tortured.

Does he react to coconut? Coconut oil is a component of SO many sunscreens and lotions that I have just given up (there is a list you can look up, but I don't have a link). Many have names that give no indication of a coconut oil base. And companies will switch ingredients between component X and component Y if they function with minimal difference. So a lotion by Whoever (TM) that you have used for years tweaked their formula to save .08 cents/100 gallons, and now you may suddenly find it causes hives when you get a new bottle.
It gets irritating. :(

i would stop using the soy butter i got wowbutter,im healthy soy butter an now 1 yr later my son got retested an is now dealing with a soy allergy on top of nut.very stressful for me with the new school year ready to begin an 90% of school food has soy in it.i would stop using it an see if it helps it cant hurt to try it can only help if it is the case

I have a fair knowledge of eczema , it can be violent all on its own without food allergy, one would think he would have other symptoms if it was food
stomach upset etc
Cat and dog allergies can be bad for eczema and being hot, salt water ocean is great for it.
While prednisone is good once stopped you can have a rebound effect even psoriasis , maybe they could taper the prednisone. Sleep overs can also aggravate skin conditions, new environment sheets etc.
I would be very surprised if cats and dogs were a no no.
good news is they usually out grow it by 20

My daughter when she was becoming allergic to many things also developed eczema. I read up and found that milk could be the culprit. I found she would break out to even the smallest amount of casein and whey that is found in most margarines. When I took her off all milk products completely she cleared up. I put her on Hemp milk. She has also done well with flax milk. I also started washing her clothes with soap nuts. These two things have kept her free of eczema now for 2 years. The switch also helped her with her asthma. I hope this helps.