After the Gym Battle, Norman will see you out of the Gym, where you’ll meet Wally and his uncle. The latter, as thanks for helping Wally on his way thus far, will hand over HM03 (Surf).
Surf is, in battle, a decent Water-type move of 90 Power that hits everyone adjacent to the user; in the field, it will let you cross waters now that you’ve actually earned the Balance Badge. Soon thereafter, you and Wally will head straight to Mauville City automatically.
Heal up here from your Gym Battle before proceeding east onto Route 118. Also teach one of your Pokémon Surf; you’ll need that. For us, it was Linoone, rounding it out as a true HM slave. You can probably Fish one if you need to.
You may even be able to learn more O-Powers from the man in the Pokémon Center, so be sure to check if just for that.
In any case, there’s a bunch of items to find and things to do thanks to being able to use Surf, so feel free to scour the region if you want them. Otherwise, see the Feather Badge chapter for going back to the main game.