I thought so, Nerite snails are hard to find in chain pet stores, most stores just sell Apple or Mystery snails or snails at all.
I think it's still fine, one Mystery Snail, 2 or 3 Ghost Shrimp (since you couldn't see three), and one Betta. I'm guessing you've cycled the tank (hopefully), along with having a filter already, with the addition of some easy live plants like Java Fern, Anubias, anytype of moss, and Marimo moss balls, and some extra water changes you'll be able to house them with no problem.
Just make sure the snail has enough food, you don't want a dead snail, they smell terrible.
If he can't finish one, just snap one in half, or smaller if needed, that's what I do with my algae wafers, my RCS tank can only finish half of a mini one.
Try not to overfeed with algae wafers either, uneaten ones will deteriorate in the water and give you more problems with water quality, if you see your snail munch on the wafer and after awhile there's leftovers, remove it.