That sounds like gerd and not cancer. :>) The thickening is likely due to the gerd. Now, you want to treat the gerd fully as Barretts esophagus is something that can happen. It's pretty uncommon happening to only 10 percent of the gazillion of people that have gerd or acid reflux but it is when the esophagus has a change in the lining and it becomes like your intestines. This would only happen if you leave your gerd untreated. Have you begun some medication now? Also, watching what and when you eat helps. Cutting down on acidic food, soda, coffee can help and not eating too late in the evening. I also found losing some pounds to be very helpful.
What kind of medicine have you started?