How to retrieve @me.com emails - selected emails not going thru

Hi!

I moved my @me.com emails to iCloud during the transition period. I can receive emails into my @me.com account and access it thru iCloud but not all of it. I did not realize this until I reached out to the sender of a very important email. She said she sent it to my @me.com account but it is not in my Inbox or Spam folder. Also, when sending emails, it is showing as @icloud.com and not @me.com So does this mean I should use @icloud.com and not @me.com due to the selective reception of emails into my Inbox?

Thank you.