Seems you peeled off a layer of your skin along with the hair on your upper lips.
If it has been less than 72 hours since this happened, you need to apply a mild steroid
cream like hydrocortisone
2-3 times a day, and also a non-perfumed heavy moisturizer which has all or any of : squalene/paraffin/petroleum jelly. apply this moisturizer 4-5 times a day.
If it has been more than 72 hours, apply just the moisturizer 4-5 times a day.
Protect the area from sun exposure, use a heavy sunblock. whenever you go out, even if it is not sunny outside.
Do NOT pick at the dry, darkened skin. Let it peel of on its own. It will feel slightly awkward for a few days because the dry, dead skin might be hanging there, but if you peel it off manually, the skin underneath might develop pigmentation (dark spots)
Keep applying the moisturizer and sunscreen till the skin has completely returned to its normal texture and colour.