Schools sign rental contracts when they lease apartments for NETs. It is difficult, but not impossible, to change such a contract or even break it.
The only EPIK teacher whom I know for certain who did change apartments did so because they were assaulted in the ground (first) floor apartment their school originally had leased for them. It was an ugly scene from what I heard. That NET didn't even ask to be moved. The school decided to move her to a safer apartment on a higher floor, and just told her she was moving, after which a large group of that school's teachers descended upon that NETs original apartment and moved her right out on the spot to the other, "safer" apartment.
Frankly, you should try to work this out with your school first. I think you'd be better off looking for a way to have your apartment steam cleaned. I would ask your school to at least help to pay for.