First of all, have you asked your doctor about it? It sounds super sensitive and it is likely reacting to something/things that you are using. Soap, laundry detergent or softener, sleeves, etc... Sometimes the sun can cause problems. Make sure you have enough Vitamin D in your system, just to be sure.
The triple antibiotic ointment/cream (aka polysporin) with pain relief is what I would try first. The pain relief comes from pramoxine and is quite helpful.
If you have already tried this, and possibly allergy ointment (benadryl makes one I think), you can try some other things. If the skin is NOT open like a wound that hasn't scabbed yet, you can try BurnJel Plus. It is in the first aid section of Walmart, by the antibiotic ointment. BurnJel Plus has tea tree oil in it, along with lidocaine. I have found it to help quite a few skin problems. We have used it on burns and it is excellent, but it helps so much more than just burns. It helps heal sores and when my scars get itchy and irritated this seems to really soothe them. If there is infection, the tea tree oil in it is very effective at getting rid of it.
I also recommend some natural remedies. Emu oil is great for scars and sores and all types of rashes except poison ive/oak/sumac. Not sure why/how it helps, but it is great. Pumpkin seed oil is also wonderful. It is packed with antioxidants and really speeds healing and soothes irritation and inflammation. You can also use your pumpkin seed oil for cooking - just google recipes using pumpkin seed oil. It adds a nutty flavor and a ton of antioxidants and other things that are excellent for your health.
If you think there is infection or something else tea tree oil can help, mix a few drops into a teaspoon or two of emu oil and store it in a little container. Keepclosed tightly, away from children, store it out of light (in a drawer or cabinet) and use it a couple of times a day (or after you wash your hands each time) and use as often as needed.
You can get the supplies on ebay if they are not sold locally. be sure to use 100% shea butter and not some jar of stuff that says shea butter but has a bunch of other ingredients.