I've had acid reflux for a lot longer than I've had these stupid anxiety attacks (I think). I suppose it could be that I've always had anxiety, and it used to manifest itself as reflux.
Anyway, mine can last a LOT longer than an hour. I'm on Prevacid and sometimes use a couple of OTC things to help out, mainly Maalox Plus tablets and Pepto. Sometimes I eat those Maalox like candy but I wouldn't recommend that because it'll introduce its own set of problems if you take too many. My doctor has said I could use Pepcid, Tagamet, etc, in combination with the Prevacid and Maalox but I've never tried that. As crazy as this sounds, sometimes eating will help me at least for a few minutes. This could be my imagination, but eating starchy things like toast and crackers seem to absorb the acid or at least give your stomach something else to do besides making you miserable.
When acid reflux gets really bad it can definitely cause stress. You can never be comfortable when it's severe. One tidbit of advice I can give you is that you shouldn't try to make yourself burp. It'll happen naturally if you need to.
Here are a few things that've definitely helped me. A lot of it is common advice:
Raise your bed at least a few inches.
Make sure you get enough sleep.
Avoid stress while eating, and directly afterwards if possible
Hope this helps you.