Go forth. Make it, explore it, find your foothold, do research, use personal experience to your advantage and if you don't have that, get out there and talk to people with experience (be courteous, be kind, respect boundaries). It really shouldn't be a "you're on thin ice, mister!?" topic because as sucky as it is to suffer mental illness, it's amazing when addressed in webcomics by small, independent creators.
Of course, there are oceans of horrible representation in media but that's largely due to shareholders and too many producers/editors' hands in the dough.
My advice to anyone who's hesitant to keep going on their comic on this topic: It's important, even if mistakes are made, be open to change, open to information -- if you're concerned about others' reactions, it's 100% okay to keep it personal. You don't have to share your webcomic about any topic that makes you feel uncomfortable posting -- just keep creating! You'll figure out where you're going, what it's about, where your interest lies in time.