Lee is Looking for an Apartment to Rent

My fiancé and I, both females, just moved to Rochester from Syracuse because I received a job offer. We currently reside with my family here but I was just informed they plan on moving the first week of February, they didn't want to say anything until it was confirmed and so now we're finding out we only have a month. Problem is I don't start my job until January 5 and my partner doesn't start her job until January 9th. 2-3 weeks of pay before we both have to be out and that will likely only get us first months rent but not enough for security deposit as well so we're looking for a room. We do have 2 cats, one is a registered ESA/Service animal and I have documentation for her. We are open to a room or teaming up with someone to get an apartment together to save money all around if that helps anyone.