There is such thing as too many tums/maalox, whatever. They can cause constipation! That's the only side effect that I know of, but it's a pretty bad one if you have GERD. You didn't say how many Tums you take, but it's enough to do that you might consider backing off a little.
You could try a proton pump inhibitor like Prevacid or Nexium. Your doctor will have to write a script, of course. Others here swear by that DGL licorice.
I'm on Prevacid but am tapering off at the moment. I have the feeling it's causing some side effects in me, but I'm not sure. Only one way to find out. Everyone's different, though. You may not have any side effects at all on one of the PPI's.