In a worst case scenario it could be acid reflux. I've had that for years though and have been fine, so you need not worry. If you get a lot of bloating and gas, or ever feel like your pills get stuck in your throat or that your food isn't going down, that could be another indication. Anxiety can make your stomach work over time.
It's no emergency by any stretch, just mention it to your doctor. Also, try raising the head of your bed by 6 inches with wooden blocks and see if the taste is there when you wake up. I raised my bed and it's done wonders for me, and I'm also on a prescription acid reducer.
All things considered, I firmly believe you have nothing to worry about that your next doctors exam can't remedy. :) You'll be just fine.