Absolutely, antacids can increase constipation. I dealt with that for years (occasional use , Tums, Rolaids, Mylanta, etc. mostly for upset stomach, not as much for heartburn).
It throws off the acid balance in your stomach, which interferes with digestion. Also, they tend to be mostly mineral (ie. calcium) which themselves ard difficult to digest.
If there is truly an excess of acid, it may not affect you as badly. Over the past couple years I have experienced more heartburn and acid reflux, but along the way learned that I was actually deficient in stomach acid. So taking antacids messed me up further.
Constipation can increase acid reflux because if nothing is moving and you keep filling the stomach, stomach fluids have no where to go but up. This is made easier if you have a hiatal hernia, as I do, which is when your stomach protudes through the sphincter muscle meant to close the stomach up.
I control my acid reflux through limiting the quantity of food I eat at one time (my doctor said stop when I think I am two thirds full), and minimize bending over after filling up. I also sleep on a ramped bedded (very good for eliminating overnight reflux). But it helps the most when my bowels are moving properly.
I did go through a healing process for some major internal issues with the help of a professional, with mostly diet changes and supplements. As a result I have not used any antacids for over 14 months and don't anticipate using them again. It may not work for all, but it works for me.
Drink plenty of warm water, try a tablespoon or two sesame oil in your food, of course fiber, and do some abdominal twists and stretches to help things move. Avoid dairy, beef and pork. Take in more liquid, less solids until things are going again.