For what it's worth (and this is just my opinion), I doubt you'll be labeled as "psycho" or become "the special patient". Therapists are there to help, not to judge
I don't think your therapist will think you're lying (or even exaggerating) as long as you're honest. Therapists can definitely smell b_llshit when they see it, and they can tell when someone is being truthful. After all, if you make a lie, you have to make another lie to cover up that lie, then you have to make ANOTHER a lie to cover up THAT lie. It keeps going and going until you can't keep track of your lies. So yes, a therapist can easily tell when someone is lying or not. Lying always catches up to people at some point!
Also, I don't think you'll be hospitalized again just for being honest. They will hospitalize you if they think you're a danger to yourself or to others, and at that point, it's what's best for you.