Before jumping to meds here's some things to try/ keep in mind.
When they poke us they are nice enough to poke us with whatever gunk they have on them and whatever we have on our skin.
Cold water, before and after. But not necessarily soap and water right before. Gentle soap.
Well hydrated skin takes the pokes better. And really rough skin doesn't seem to be bothered much by it.
Oatmeal is soothing to us as well so an oatmeal soap might be of some relief, also aloe could provide some relief.
You might want to take a wash rag and give Finn a quick wipe before really bonding. This may be especially true with the dig box and anything like that.
If nothing is giving you relief, try Hydrocortizone cream or a lotion for itchy skin conditions.
Who all shares a room with Finn? The reptiles shouldn't have a direct effect but possibly some bedding or dust could be drifting it's way to his cage and onto him. If Pepper is one of his neighbors, the dander may be a factor.
For me the cold water is a big help, but you've seen me suggest it so probably have tried it and wouldn't post this unless it wasn't working for you.
Also, some body parts are more sensitive than others. If one of my hedgehogs is sitting on my belly and pokes, I'll have welts for a week.