Okay, but ice isn't good for this; ~~it's a chemical burn, and~~ capsaicin is fat-soluble. You ideally want something like milk. Meanwhile, on your hands (assuming some of it got on those), you want to cover your hands in oil and then wash them with dish soap (and once those are clean, if there's residual burning, you can use topical pain treatments).
Edit: My understanding of the term "chemical burn" was mistaken. Thanks to @Nurse_Robot@lemmy.world for calling me out on this. I didn't know it had to be corrosive or cytotoxic to be a "chemical burn"; I thought irritants generally were included.
Edit 2: Actually, looking further into this, I'm not so sure I was technically wrong at the level of capsaicin you'd be exposing yourself to with a Carolina Reaper. Capsaicin can be cytotoxic. I wonder now if very minor nerve death occurs at this level of spice. Either way, that's not the main problem if it's even happening; my comment was wrong regardless of possible technical accuracy.