Most of the times you can see the status of an exchange directly from the exchange history in the app. For this, open the exchange section in the app, and at the top right corner of the screen select "Exchange history". There you will find a list of your exchanges made in the app and can select them to get more details.
If an entry is still "waiting for deposit" or "waiting for exchange", it's possible that your device didn't automatically update the exchange status. In this case you can press the refresh button at the top of the screen to force a new refresh.
Coinomi does not store any user information on its servers. There are no central logs or backups of your exchanges. Instead, the exchange history is stored locally. Reinstalling the app or restoring on a different device will restore all balances, but not the list of exchanges.