You cannot check your purchase history from within the app. 
Purchases are processed in your app's store. 
Please see the link below for more information.

AppStore：https://support.apple.com/en-us/118212?device-type=mac

Google Play：https://support.google.com/googleplay/answer/2850369?hl=en

If your purchased items are not reflected, please also read "The purchased items are not reflected."