Honestly if you are even considering inpatient you probably need to go. When I even think I might want to go in, I am in serious mental trouble.
As for missing classes, most likely you will end up withdrawing for this semester. Don't worry. You can use hospitalization as your medical reason. Uni or college doesn't even need to know diagnosis or anything. Medical time off is much different than dropping out. That you are admitted to the hospital is all they usually need. Most state unis (i have most experience with) will give you Recovery time too and work with you about how soon you want to return and what about classes you were enrolled in.
But right now you need to focus on getting help for your mental health. Take care of yourself. Your education can pause while you get safe and taken care of.