edit: Now I think on it, actually, depending on (variables), you might need a specialist visit more than a PCP visit for some antacids. Shame on me for assuming it's just unmanaged acid reflux.
Kidney stones scare me, I've heard horror stories of the pain it causes. Is half a tums alright after acidic meals? How much more likely am I to develop kidney stones?
Speaking in broadest generalities:
1. The kidney stone risk a/w calcium carbonate intake has not been well-quantified. In a couple of studies of post-menopausal women the risk elevation was estimated to be in the range of a 20% bump. It has not been quantified any better in any other demographic segment, that I am aware of (nota bene: I'm not a nephrologist or urologist).
2. Timing-wise, the closer to the bulk of the meal the tums goes in, the better. You get calcium stones due to calcium oxalate crystal formation - when you take the calcium with food, the calcium is prone to crystallize with oxalate in the gut and get shat out, rather than both getting absorbed and crystallizing in the urinary tract.
3. The other risk of constant tums supplementation is an acid-base condition known as milk-alkali syndrome (a combination of hypercalcemia and metabolic alkalosis). Please, get your basic bloodwork done.
4. I can't speak more usefully without understanding what medications you're on and the timing of their administration. I'd strongly recommend having that discussion with a trusted physician, because this really shouldn't be your baseline condition, full stop. If you want to share more details so that I could suggest more specifically what sort of specialist you should see, if you don't currently have a trusted physician, let me know, and I'll arrange a way of sharing contact information.
There have been some very weak recent studies on PPIs and long-term dementia risk that look very flimsy. Other than that, I’m unaware of “long term damage.”