That’s a tough place.
In Cata, at your level, you need to raid to progress. It’s not like Retail, where you would have M+ as an option.
I would normally suggest looking for Discords, but I just did a quick search and found nothing useful for Cataclysm.
I would have thought, though, with Cata winding down and Mists on the horizon, that guilds would find they have people dropping out, and might be scraping for replacements.
I’m not sure that guilds have ever been welcoming to new members. You just kind of stick around until you’re not the new guy any more.
I’m sorry I don’t have anything more helpfiul to give you, but at least know that it’s not you - it’s the way the game is structured.