I tried zinc carnosine when I was dealing with constant GERD -- that form of zinc apparently helps a lot of people with stomach/digestive issues, but it made my gastrointestinal symptoms worse.
I gave it a couple of good tries that lasted several weeks each, but it was definitely making me feel worse.
I then tried a couple of other types of zinc.
The one that worked out the best for me was Solgar's Chelated Zinc (zinc glycinate amino acid chelate). It comes in a 22 mg tablet.
I usually take 2/3rds of a tablet a day (15 mg), but sometimes I'll take a whole one. It's not given me any gastrointestinal problems.
Note that the front-facing label does not specify that it's the glycinate version in particular, but on the back it is spelled out. (Solgar sells other forms of zinc, so it's a good idea to check out the back of the label to be sure of which version you are buying.)
They offer 2 bottle sizes, 100 tablets and 250 tablets.
Just yesterday, I ordered a bottle of the 250-size for less than $10 on Amazon. (In the past, I have seen it at IHerb for about $17 and at Swanson for somewhere in-between, so it pays to shop around.)
I've read that supplemental zinc is easiest to digest/assimilate if taken with a meat-protein-containing meal
(apparently dairy-based protein, like cheese, counts),
and that it's better not to take it at the same time as chromium or with a lot of phytates/grains.