First of all take a deep breath. RELAX. You are doing everything right. It doesn't matter how many homes are on the market. A home that is in good repair, with new carpet, fresh paint , great curb appeal and one that is properly staged will command a higher price and sell faster than anything that is "dumped" on the market. You don't say where you are but here in Dallas, banks are hiring stagers to get foreclosed homes ready before they put them on the market. They don't just release a ton of homes at once. Bankers are in business to make money.
If you are worried, get more than one opinion from one Realtor. Get SEVERAL opinions from SEVERAL Realtors. Then, call up some banks with properties they need to release and ask for a preview. Do some research. They don't have to know you are not a serious buyer.
The bottom line is the purchase of a home is largely emotional. People fall in love with houses. They visualize raising their children, throwing parties, celebrating Christmas. One of the things I always hear, besides "Where will the flat screen go?" Is "Oh we can put the Christmas tree there!" People are not out searching for ONLY the lowest price. They are searching for the least hassle! No one wants to deal with home repairs and no one wants to have to install carpet and repaint. Buyers today want to walk into a house that is move-in ready. So, you have NO competition really.
Follow your instincts and interview several Realtors until you find one that has the same outlook! Let us know what happens!