I'm not sure how many times I'll end up doing this before I learn. Maybe if I post it here it will help me remember, if nothing else than through public humiliation.
When chopping, and especially when de-seeding any sort of hot peppers, DO NOT DO IT WITH YOUR BARE HANDS.
The burn is delayed, so you may think, "Oh, I'll be fine," and then later the pain sets in. And no, it is not just a warm feeling, it is PAIN.
And nothing cures it but time. Not milk or yogurt or sour cream or butter. Not soap or lotion or vegetable oil or rubbing alcohol or minty mouthwash.
Not W4-40 or Goo Gone or even chlorine bleach!
All substances added will, at best, provide temporary relief through mere cooling, and at worst, in the case of the stuff I tried when getting more desperate, will damage your skin and maybe make the burn worse.
All you can do is sit there with cold packs on your hands and grit your teeth and wait until the burn wears off. This takes something like 12 hours. Hope you don't have to be anywhere in the morning because you won't sleep well.
Do not be fooled by the delayed reaction. You WILL pay for it later. Repeat after me: Gloves are worth it. Gloves are worth it. Gloves are worth it.
Capsaicin, you got me this time, but next time I will be prepared. And I do now have a good batch of jalapeno seeds for planting next year, but oh boy, those were hard won.