I can relate. Even though I don't do much welding, I have a bottle of pure aloe from the pharmacy that I keep in the shop. Nothing better for a burn.
One dumb move I repeated a few times back in the day was to overfill my Zippo and put it back into my pocket.
On the same theme, I was also known to put rags with gas on them from cleaning parts, etc. back into my hip pocket. Problem w/both of these smooth moves is by the time you feel the first tingle of the burn to come, it's too darned late to do anything- the damage is done, it just takes a few more minutes before the burn well and truly sets in. Only time will help then.