I had the exact opposite experience! How weird. I was just thinking how I haven't had any problems with heartburn since I started SB. I had it very frequently - like 4-5 days a week, and now I have nothing! I'm sure you could take some antacid. I doubt there is any sugar in that!
I took some antacid and it had a little sugar in it but I figure it's worth it. My stomach doesn't really hurt anymore but now I've been running back and forth to the bathroom (You're welcome for the TMI!).
I had awful heartburn when I was pregnant with my second and I found doing yoga right before bed helped out (mine hit at nighttime). Are you eating too much at one sitting? Could you eat more, smaller meals? Are you drinking any milk? That typically helps. Maybe watch your quantities of tomatoes, peppers, and other trigger foods.