I use burts bees lip balm in the little tin can. There is a stick medicated version but I found for my dry lips the tin can one worked better and felt better. I found this O’keeffe’s products are great for dry skin and apparently they sell lip balm. I’ve never tried it but on this site, it says it takes up to two weeks of application to start to see results. For you, it may be longer.
As others said, this is years of damage so I wouldn’t expect quick results, but I also don’t think vaseline is that great for lips. It always makes my lips swell so I don’t care for it.
Even for lip sunburns, it can take 3 days to 14 days to recover depending on the damage.
Also, I would suggest drinking plenty of water and taking vitamins like C and A and E to help with skin repair.
Of course, I am not a doctor and they may recommend something stronger that will work quicker so it wouldn’t hurt to check with your physician.