Insane Asylum

It is definitely possible to be wrongfully entered into an insane asylum (even against your will). Once you're inside, unless you've got contacts outside (and people who would realize that you're missing), you probably won't be getting released anytime soon.

Even if you knew someone, it'd still be pretty hard to get you out. The workers/supervisors most likely won't even admit if you're there or not.

It's also basically impossible to prove that you aren't insane. The more you panic the more reasons they'll have to keep you locked up / strapped down / sedated.

Of course there's the possibility that you're actually insane and part of your condition is that layer of self denial.