If a listing is featured on "local realty websites" but is NOT listed on Fannie Mae's website, then I would question the source of of your information. Which websites are you looking at? If it's a current Fannie Mae property, then it will be on Fannie Mae's website. If, however, you're using a 3rd party website like Zillow or Trulia, then the information may not be up-to-date. Third-party websites are less accurate than Realtor websites. If you spend a lot of time on third-party websites you've likely discovered that the information may be weeks or even months out of date.
My best advice is; seek help from a Realtor. In most cases, you won't have to pay for the services of an agent. Realtors are paid by the seller when a sale closes. (Discount or fee-for-service Realtors are paid by you.)
The real estate (agent) database is highly accurate. You'll save a lot of time and frustration if you seek the best and most up-to-date information. Talk to a Realtor.