The rat thing is scary, it's also a health issue. If the landlord doesn't take care of that, call the local Health Department.
I've never had to live around rats. Mice yes, rats no. Ugh.
Stick it out for the time being. This is your first experience living independent of your parents, isn't it? (apologies if I am mistaken, my memory isn't the greatest) Use it to resolve that in future, you will have better conditions. One step at a time. Even though you are on disability, there are a range of living situations, some that you have to be on a long waiting list for. Get on such lists!
I can't comment on the overnight stay at a hospital, I'm not familiar with a program like that. What are your symptoms for which they would admit you? It would be nice... is not enough of a reason, usually.
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A finger in every pie.