A co-signer typically only helps if you are having trouble qualifying on your income. It doesn't normally help with regards to lower credit scores.
Were you declined because your middle credit scores were only 640 or based off of the collections? If it was simply due to scores then check around because although a lot of lenders require all borrowers to have middle credit scores above 660, there are some out there that will still go down lower than that.
If you were declined by FHA's underwriting system then that is likely due to the timeshare and you will probably have to pay that off. An installment debt, especially housing related like a timeshare, is looked at much more seriously than a medical bill.
At any rate I would check around with a couple local reputable lenders and get a second opinion and some insight into exactly why you werent able to get preapproved.
Best of luck!