Which app is that exactly? You coulse use a third party exchange to sell your Bitcoins for cash.
e.g:
Coinbase,
LocalBitcoins or
Kraken.
I thought the app I'm using WAS a 3rd party? But I am not sure.
I assume you are using this (
https://play.google.com/store/apps/details?id=de.schildbach.wallet&hl=en). Most (All) Bitcoin wallets only functions as a wallet and not as an exchange. They are only used for transacting Bitcoins but not to transact from Bitcoin to fiat. You have to use an exchange for that. Coinbase, LocalBitcoins, Bitfinex, Bitstamp are various examples.