Definitely mention it to your doctor and maybe have some tests if it never goes away. I've never been pregnant but have been getting heartburn at night for a couple of years. My doctor did a barium swallow and it turns out that I have a hiatal hernia. It wasn't at the point of needing surgery and I control the symptoms with medication, but if it gets worse I will need surgery.
Talk to your doctor about going on a proton pump inhibitor (ie, pantaloc, nexium, pariet) as they often can heal areas that are sore. If it is gerd, those meds are also great for long term use, and give great relief from heartburn. They work much better than most OTC products. My H uses pantaloc and its honestly been life changing for him. He's no longer in pain and stomach upset.