Breathing feels constricted when I'm completely upright but opens up when I tilt my head down. Could this be related to GERD? Anything else?

It could be GERD... it may be, Also possibly an inflammation or even enlargement of the tonsils could be doing it, as if you move the neck a certain way, the tonsils could shift for example and allow more air flow to pass. Al just guesses. Get and evaluation to see why you are having breathing issues. Good luck.