Hello and welcome, zhey KingAlanI.
Yes, investigating a conlang is kinda mad pursuit, but it has it's perks, and can even be a very nice sort of abstract and philosophical starting point on a more linguistics-centered language adventures. I find it a wonderful diversion, engaging on multiple levels and in many dimensions. I'm not much of a language person either (though I've learned this English language to a passable level, being a Finnish speaker originally), but after a couple of years with Dothraki, you may notice I'm not a total linguistics newbie anymore.
Sidenote: Writing fanfic it's safer to idetify yourself as a GoT fan. GRRM is somewhat famous in asking his fans not to make fanfic, and this wish has been much respected amongst the fans. But IMO greenligthing a derivative work as big as a major HBO series pretty much surrenders that fight. GoT lives in social media with such an unquenchable flame and is so much a work on its own rights that there's just no way, no reason, no argument to limit the scope of derivative works.