Heres a link to gaijin houses Gaijin House´s:
Home
the one i stayed (quite nice!)
Oakhouse | Guest House Tokyo, guesthouse, room rent in Japan
however i´m not sure if you can manage to pay them either... its at least, i guess, 40000yen a month for a dorm room (if you are lucky to find anything) and youth hostels will usually be more expensive than that for a whole month. Your best chance would be to find someone sharing a room in a gaijinhouse with you, this would be around 30000yen a month, but i wouldn´t do that with anyone i don´t know. Isn´t there the possibility to rent you current apartment for 1 more month? Have you asked your school for advice?