Chuck all your gloves into a bag, and wear a new pair for a week.
If the rash eases, ya know it was the gloves re-contaminating your wrists. If not, ya got something else going on.
It's not unusual to have localized allergic reactions, in areas that have been affected previously,when exposed to a very small amount of the irritant.
You on any meds?
It's goofy, but some Meds have oddball side effects like localized reactions.
Laundry detergent? Fabric softener? Some folks react to the laundry chem.
Localized reactions to other irritants then the original also can happen. Had that happen with a pair of boots that got soaked with herbicide..drove me nuts trying to figure out how the hell I was getting Poison Ivy on my feet in January. Went through a couple dozen pairs of socks before the Allergist figured it out.
On the wood issue, if you think you are, be carefull and get tested.
This time of year the air is literally toxic if you are allergic to tree pollen, and can kill you. I found out the hard way, and it ain't fun.
It takes the doc about 30min to poke the hell outta ya and then tell you exactly what you react to, and then explain how to deal with it.
Best of luck to ya in narrowing things down.
Stay safe!
Dingeryote