First I want to say how sorry I am that you are going through this...it's so difficult when you have to make a decision when both of the choices are horrible.
Let me put it to you this way and see if it helps at all...
The first choice, continue what you're doing: Okay, so say you continue at the rate you are going...your lips will never heal (so far no one has documented proof of truly recovering this way) and they get worse and worse each month...and you live like that for your ENTIRE life...
The second choice, you leave your lips alone and go through several months of truly horrible LOOKING lips. While you do this you will be embarrassed up to the sky and will have the most difficult time just getting through the grocery store...but your lips will feel great underneath all of that protection, they will actually feel wonderful at times...you may not be able to smile, but letting your body heal itself is a wonderful feeling. And after several months, which will most definitely feel like decades, you'll be completely healed and will never have to look at chapstick again, let alone everyone you know will have forgotten you even had bad lips once you are finished...so it's a win win if you ask me. You will be the only one who ever thinks about what your lips used to look like once you finish this battle.
If you ask me, it seems like choice number two has a lot to offer. As for your job, what I did since I was a server (as my second job) was wear a beard guard over my mouth so no one could see me while I worked, they asked why I was wearing it like that and I just said I wanted to. No one really said much to me. It sure beat the embarrassment of them actually seeing what was under. If you are really going to go this route and are in school I would suggest taking online only classes for the next couple semesters, or just taking a break, a BREAK won't put you back much, just make sure that you do return! And about the job if you seriously have to have it then ask to do something where you aren't in front of customers, if you are at a restauant or fast food, do the fryer or make the sandwhiches or something in the cooking area. I was a server assistant at my restaraunt job where I just set up trays to be ran. My main job I am on the phone so I don't have to do anything there.
I am on week 14 now and my lips are getting better each week, SLOWLY, but SURELY. I can assure you of that.
Good luck, and when the time is right and you have enough motivation, you will make the decision to beat peeling lips!