Can someone be reading my iMessages? Someone has told me they can read my messages I send through iMessage. Is what they are saying true? Can someone do this?
They can only view this information if they are logged into your account on their iDevice.  For example, an iPhone, iPad and MacBook all on the same account will receive all messages sent or received from the other machines (barring a lack of network connectivity).

My suggestion to you is to change your password. They will be prompted for the new password and will no longer be able to view new messages that you send or receive through iMessage. I would also change the password associated with your email account if you use similar or identical passwords for these accounts.

Existing messages that they have captured will not be removed from their device, so be wary — anything incriminating that has already been gathered is in their hands.