Only your @me.com address is affected. No other email account has anything to do with it.
A MobileMe account must migrated to iCloud at http://me.com/move before MobileMe terminates at some time tomorrorw. If you do not do this you will lose the account, but I emphasize that no other email accounts are affected in any way. The termination of MobileMe was announced over a year ago; you need to do this migration as soon as possible.