[...

Schadenfreude: making the world a better place to be.]

There are places called Centers that will heal your Pokémon for free - they'll do it an unlimited number of times, as well, with no charge that I know of. They're only in the cities, though, and so not much help on the actual routes.

[...hmmm.]

There's a computer situated in all of those Centers, where you can access your personal storage boxes; check yours when you get to Cherrygrove.