Drinking more water won’t help, unless you are actually dehydrated, I mean thirsty all of the time. They have shown oer and over again that once you are hydrated and start needing to pee all of the time, you aren’t adding more water/hydration to your skin. I am not saying it isn’t good to drink water to help flush your system/kidneys of toxins in the body and to avoid kidney stones, but it isn’t going to help your lips if you are already taking in sufficient fluids.
Put vaseline on your lips at night before bed to heal them, or you can also buy products to moisturize and heal lips from cosmetic counters. Chanel used to have a very good one, I don’t know what they have now, but I would try the vaseline first, much less expensive. Then use chapstick during the day to keep them protected. Don’t lick your lips.