Hi C4rm3l,
Thanks for coming to Apple Support Communities for help today with your iOS Mail app. It sounds like you select All Inboxes and but if you exit the app and come back you are only in your Gmail inbox. You have to go back and get into All Inboxes again or the AOL inbox to see your AOL mail.
Have you restarted your iPhone since this started: Restart your iPhone?
You can also try that in combination with force closing the Mail app: How to force an app to close on your iPhone, iPad, or iPod touch.
If that doesn't resolve the issue, you can try removing the Mail accounts in Settings > Passwords & Accounts and restart once more. After that, set up the accounts again and test: Add an email account to your iPhone, iPad, or iPod touch.
Let us know how it goes.
Have a great weekend!