Why are all of my email passwords unrecognized?

I went to the Atlanta Lenox store for help with my GF on Sunday. Michael could not have been more helpful. However, once I returned home each of my three email accounts started to "act up." Each time I tried to enter one of the accounts, I received a message to enter my password. I did so each time and many times thereafter only to receive a message "Password invalid" or "password unrecognizeable."

I have deleted each account from my MacBook Air and from my Iphone 5. Each device is now "acting up." Has anyone experienced such disturbances and what should I do to correct the issue? Thanks in advance for any suggestions.

JT Newton