Cat got my thumb instead of the toy (infected wound)

so, after the incident I cleaned it with water and let it be for 3 days, but im guessing because its right were the thumb folds, it got infected.

yesterday night i tried to pop it like a pimple and some pus came out

how should i proceed? wash it often with soap and water or should i keep it dry? i have hydrogen peroxide and eosina at home if needed, re-opening the wound to clean it is a bad idea?

my doc prescribed antibiotics for a cat scratch I received he advised cat saliva sometimes contain bacteria that can lead to infections