Welcome to the forums. Yes, it is possible to get medical collections deleted from your credit reports. In order to do this you need to negotiate with the collection agency that is reporting your debt. The first thing you need to do is get a copy of your credit report to get the latest and most accurate information. You can get a free yearly credit report at annualcreditreport.com (this is the official site).
The next step would be to negotiate a “pay for delete” with the collection agency. This means you write them a letter asking to delete your tradeline in exchange for your payment. You can offer to pay in full (less negotiation involved), or pay a lump sum or make arrangements to start a payment plan. It is very important that you try to get this in writing to have proof in case the agency “forgets” to honor your deal.
I was able to get two medical collections deleted from my credit reports this way. Here’s an example of a “pay for delete” letter: http://credit.about.com/od/debtcollection/a/payfordelete.htm