I'll second Andy's comment. Yes, erosions in the esophagus can heal, but its a long process. The omeprazole will not heal anything. It only helps to prevent further damage by reducing stomach acid. But learn of its long term side effects. You should supplement with calcium, magnesium, Vitamin D2, D3, and B12 while on it.
Gaviscon and melatonin are also good. But keep in mind that, as long as your are on omeprazole, Gaviscon's main benefit will be the alginic acid that forms a "raft" that stays on top of your stomach contents, keeping it from rising to the throat. So it will not be of much help taking it at bedtime. When you lie down your stomach contents goes horizontal with you, putting the "top", and the raft, in a different place that wont protect your throat. If night time reflux is where your issues are, much better to make sure you do not eat or drink within 3 hours of bed time, and raise the head of the bed 4-6 inches. Not just pillows- raise the mattress.
I was diagnosed with Barrett's short segments last Sept, and have my follow up endoscopy in June. Was on Zantac for a while but got off that as the damage to my throat has come only from nighttime reflux while lying down. I never have heartburn during the day. So I take Life Extension version of Gaviscon after dinner. I also take melatonin, and have for years, but just to help me sleep through the night due to an enlarged prostate. Melatonin is a powerful antioxidant as well, but I don't expect you need it for sleeping. It won't hurt, but at your age, your body should still be producing plenty of it. Not so for me.
Other things I take to hopefully help heal my esophagus are manuka honey, DGL, and beta carotene. After an extensive search for Barretts treatments, I could find no real recommendations. I did come up with one, and only one, scientific study that was done in 2000, and then done again in 2012 by a different team, involving beta carotene in does of 25mg/day. The first study was declared invalid due to procedural mistakes. The second one did not have those errors, and the results were just as promising. But this is a very high dose. Higher than recommended as a dietary supplement, and there can be some side effects of too much, so please proceed with caution if you take this route. The study involved only 6 people, but all 6 saw their Barrett's segments decrease in length and number, and two people had them disappear entirely. I hate to base much hope on such a small single study, but the dramatic result made me feel it was worthwhile to increase the level of a nutrient that I needed to get anyway; and beta carotene is known to act on the outer layers of skin, so it all made perfect sense.
Good luck and don't stress over it. Stress can cause heartburn