I guess the previous owner had an old bathtub/tiles sprayed with some
kind of white enamel paint or something because some of the edges of the
tiles that are hit by water constantly are starting to peel/crack off
exposing the original ugly tile underneath.

I bought "porc-a-fix" at home depot and was going to give that a try to
prevent water from getting into the tiles and peeling it inside out, but
is there a more common way to touch-up the tiles treated with such an
overcoat? Are there spray-on glossy white enamel paints I should use
instead?

Any tips/suggestions much appreciated!