Yes, it stinks...but you now need to take some precious time to do a search (again) online for housing in that area. Sometimes people get lucky looking that way and you don't have to travel back and forth until you actually see something you are truly interested in and can work the real estate agent listed on that particular house.
Also, did HR spell out exactly what the relocation expense money can be used for? I don't know all that much about private industry, but you will need to check to see if the money they are providing for relocation is something you'll have to pay taxes on. In some instances, you won't get the money up front, but paid at the end once you submit your receipts, etc. Here's my two cents, you may need to bite the bullet and ask you dad for a loan to help offset your moving/security deposit w/the understanding that you will reimburse him as soon as you are reimbursed by the company.
Again, it's my two cents. At some point, you are going to need to ask your parents for help on this move in order to get moved and ready to rock and roll on October 1st.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.