To add to BREAKINGBEN...
So what is there besides OT?
Well, Pokemon
does have a massive cast of canon characters that are never or almost never written about. You can always create a story about one of them. There's Grace, the girl with the Medicham who competed against May and who currently engages in contests, if you want someone like a trainer but still fairly different. (Because, hey, OT stories don't involve the backstage drama of a beauty pageant.) There's Domino and every other Rocket agent, who all for some reason aren't taken advantage of, even though you've got a ton of potential there with stories about thief-heroes. Heck, there's even my favorite, Bill, who's a Pokemon researcher and therefore is
begging for tons of nutty sci-fi adventures. (I mean, come on. Pokemon meets
Jurassic Park? Pokemon meets
Invasion of the Body Snatchers? Pokemon meets
The Blob? Why have these never actually come to being?)
So, really, you don't even have to create an original character if you don't want to. Pokemon's one of those odd fandoms where people tend to be shy around using the huge cast of characters canon already gives you, unlike in every other fandom where most people cling like none other to the canon cast and maybe insert one or two original characters (who are often Mary Sues anyway). Pokemon canon doesn't even bother trying to give a number of the characters it creates solid characterizations, so you actually have plenty of freedom of choice and creativity -- more so than a lot of other fandoms out there. It's just that a lot of people don't even consider that there
are untold stories in the Pokemon fandom and attempt to create a new puppet for a new OT story.
Otherwise, as BREAKINGBEN said, there's a lot of other genres that the Pokemon fandom can cover. Your original character might not even need to be a new trainer. Like characters, Pokemon canon offers a lot of flexibility with occupations as well. Not only are there coordinators, thieves, and researchers, but there's also breeders, watchers, gym leaders, collectors, hunters/poachers, nurses, and even occupations that don't actually work with Pokemon directly but instead maybe on the side, like construction workers directing a bunch of Fighting-type Pokemon. And even then, there's also the possibility of working with older trainers -- people who are already established as trainers and are simply going on an adventure other than your standard journey. At the risk of ego tripping, all of the characters in my pet fanfiction (in my sig) are original trainers, but they're all also established. Thus, the fic isn't about a journey where someone starts off from a town with a new Pokemon by their side. It's about how they use Pokemon to accomplish what it is they set out to do. So, yes, it's perfectly possible to write original characters in the Pokemon universe, but you just have to stretch your imagination with it and will yourself to find something else for a trainer to do besides start a journey with their starters by their sides.
Likewise, varied occupations come varied genres. A scientist, as I've said before, might open up a world of science fiction for you. Romance may come from coordinators (and often does, actually), breeders, what have you. Mystery for police officers like Officer Jenny.
Really, the world of Pokemon fanfiction is vast and full of variety. All you need to do is think outside the box by looking at just the basics that you have to work with. For a Pokemon fanfiction, you only need one thing after all: Pokemon. Figure out where to go from there by looking at what you can do with Pokemon. You can get some hints by looking at canon -- specifically, the people Ash or so-and-so meets along the way.
