Bikerjeane, several thoughts come to mind.

If your core muscles (abs and back are strong so you are not leaning on your hands), think about where the pressure is coming from. It may be no where near the palm of your hands.

A year ago I took a fall from my mtn bike. It has taken a yr to heal because I damaged the tendons. Any irritation causes a little swelling in my wrist which then pinches nerves cause numbness and lack of strength in my hand. The dr told me it could take a long, long time to heal but absolutely to not ride through the pain. Braking in the drops was horrendously painful but riding on the hoods was fine. I really paid attention my position and speed so I could compensate.

Changing the fit and postion from the norm: Are there any positions which don't cause the problem? Anything which cocked my wrist caused problems and since I ride road and mtn including bar ends on the latter, I had lots of positions and adjustments to test. You don't say whether this is a road bike or mtn bike. Which is it and have you really had an expert look at your position including wrist and hand positions. I get a lot of wrist pain from the common 3-5 degree bend flat bars stocked on mtnbikes and now use a 9 degree bar. Unfortunately, fixes like 9 degree bars takes an very experienced fitter or someone with a lot of bike knowledge who will think spatially and beyond the normal stuff on the LBS shelf. Ulnar Compression Syndrome will also cause the symptoms you're having. I ride with relaxed and slightly bent elbows, but I can't maintain the sharp elbow bend postion that many road racers use because I'll get symptoms much like you describe. I also like to have my road brake hoods tilted inward slightly for my hand and wrist comfort. The LBS will build the bike with these aimed straight forward unless told otherwise. On all my bikes, I'll close my eyes and kind of rotate brake levers, bars, etc. until my body says it's happy. I don't want my eyes to tell my body "this is where the component is supposed to go."

All this comes from 20 years of building up and riding tons of mtn and road bikes and being a position princess (ask my wrench boy hubby).

The gloves themselves: I have found that I get a lot of numbness from the particular gloves I wear. On the road, I hate PI GelLites because the pads cause a ridge in just the wrong spot on the pad of my thumb. My old PI White lines are much more comfortable and I'm trying some new Assos which don't have separation of the padding but a nice smooth palm. Only one short ride, but they did feel good.

Lastly get medical help and do not push through this pain. Inflammation that causes loss of strength is nothing to fool around with. Nerves are involved and unless you can determine exactly what is causing such a severe problem, you need to seek the help of a medical pro. Nerves do not rehab well. The cause of the symptoms can be nowhere near your hands.