Fomo ain't an illness, it's a fear, hence "fear of missing out". Fomo is just like a fear of heights, it's common. Mental hospitals are for people who are usually a threat to themselves, others, or people hurting them. They also have therapy for things like MPD/DID (multiple personality syndrome), severe depression with attempts and/or cuts, or more rare disorders like Alien hand syndrome or Alice in Wonderland syndrome.