Short-term room wanted: Roman in Spokane

After leaving an abusive relationship, I'm temporarily without a home. I work as a teacher's aide in Spokane and I have a steady income, but I can't find a place that will let me in without the first month, a deposit and references that I'm in the middle of replacing. I'm looking for a spare room for 3 months. I can pay $250 a month toward bills, I'm tidy and quiet, and I'd be happy to help with cooking, shopping or yard work. I have no pets, I don't smoke, and I have three personal and work references. I understand that inviting a stranger into your home is a big step. I'd be glad to meet in a public place first and to share my work details. Thanks for being kind about this.