That sounds horrible for both of you! HUGS.
I cannot possibly compare my experiences with DS to burns, but he has severe anxiety, plus sensory issues that make him feel like he's being tortured when I help him do certain everyday physical care tasks. So perhaps some of my ideas might also help in your situation?
I let him have as much control as he wants/needs. Your little guy might be too young to really participate much but if you can find some way to let him help with his own wound care, he might feel more in control of it. Maybe he gets out the medical supplies, or opens the bandage, or rubs cream on part of the wound himself (or even just elsewhere on his body), or something like that? When we feel in control of what's happening to us, it's less painful & traumatic.
When you're actually changing his bandages, find a way to make it special & more relaxing (even if he still screams the whole time). You could tell him a favorite story, put on a favorite song or TV show, follow it up with a special treat or book, whatever will be meaningful to him. Take some time before & afterward to really reconnect with him.
Most importantly: Role-play what happened to him... How he got hurt, followed by the trip to the hospital, and then home care. Get his favorite stuffed toys/dolls and have him be the doctor or the parent taking care of the sick child. You be the voice of the hurt stuffed toys (and prompt him as necessary, "I'm hurt!! Can you give me a bandage? Can I have a kiss now?") Let him put real bandages on them, wash their hands, give them pretend medicine, comfort them, etc. -- everything you do for him. Do this over & over until he loses interest or seems to have moved on. In my experience, playing out the trauma & its aftermath can really help little kids process it. Make sure you focus on the whole thing (especially how you took care of him afterward, etc.) not just the bad parts, so he can have a sense of resolution & realize he is OK now.