Any suggestions

The first photo is my lips after two days of not rubbing the skin off in the bath. This is with using lip balm during the day.
The second photo is the night after i rubbed the skin off the same day in the morning.
What i want to know is, can i try some thing (cream, or medicine) to make the swelling of the lips go down, but still keep rubbing the dead skin of every day.
So what it is i am asking, can i fight the swelling, but keep rubbing the dead skin off?
The reason i am asking this is because i need to work, and cant have this dead skin on my lips, as its clear my lips look much better with the dead skin off.
I understand i need to leave it alone to give the treatment fighting chance, but i cant go to work like this. As this is only two days, think after a weak, i will look like a freak.
So is it a losing fight to keep peeling and treating the swelling at the same time?