bleach burn... please help?

I work with bleach at work. We use a 1:10 solution. 1 part bleach, 10 parts water. We are offered big yellow cleaning gloves, but they have been eaten away by the bleach and the manager won't buy more, so i don't wear the gloves because on me they seem to just hold the bleach water inside the glove the whole time i clean. I have acquired a bleach burn on the top of my hand and on my forearm from wrist to my elbow. It's red, and hot to the touch. It looks kinda like i have hives on my hand and arm, but there are no blisters. any ideas on how to make it hurt less, and help it heal faster. In a few days it will start to itch like mad. I've gotten hives from so many things i know what to do for that, but the burn i don't know what to do for. I can't use triple antibiotic ointment because I'm allergic to it. I swell up or break out in hives depending on the part of me it is put onto.