On your original mortgage, 1-4 pages past the signature page will be a VA Rider. At the top it will say "NOTICE: THIS LOAN IS NOT ASSUMABLE WITHOUT THE APPROVAL OF THE DEPARTMENT OF VETERANS AFFAIRS."
That is a VA loan. The picture above is from a VA mortgage. The page for the VA mortgage was two pages below the original signature page of the mortgage. The pages between this and the signature page had the notary's signature and the legal description. You can get a copy of your mortgage from the public records in your county. Most Realtors will know how to look up this information. If not, then they will know a title company that can do the research for you.
A VA Short Sale is called a "Compromise Sale." According to those guidelines, they will give a complete release if a seller participates in the short sale program, and there was no "fraud, misrepresentation or bad faith" on the part of the homeowner. The bad news is that you will not be eligible for another VA loan until you repay the VA for their loss. So you may not be able to get a VA loan in the future.