Me account

You will need to be signed into the iCloud account that you moved your @me.com email to in 2012 in order to use the @me.com alias. When MobileMe was shut down in the fall of 2012, all @me.com addresses became nothing more than alias addresses for the iCloud.com account they were linked to.

See -> iCloud: About your @icloud.com, @me.com, and @mac.com email addresses - Apple Support

It’s just an alias to your @icloud.com inbox so if you have iCloud mail enabled in your account settings, your @me.com emails should show up in your iCloud email inbox.

You are welcome. Did you try the last link I posted? Try deleting the account, restart the phone, and add the account back.

What happens when you try? Error message(s)? If you go to iCloud.com/Mail using a computer browser, are the emails there?

See if anything here helps.

Mail – Setup on a device    

Mail - If you can’t send email on your iPhone, iPad, or iPod touch

Mail - If you can't receive email on your iPhone, iPad, or iPod touch  

Have you checked Settings/Screen Time for any restrictions?

You are welcome. Glad to help. If by 2 profiles you mean 2 Apple IDs, Apple IDs can't be merged. If that isn't the question, what do you mean by profiles?