How do I get rid of an old email address?

I need to get rid of an old email address that was being hacked. I've had a new address for over a year and still things like my Apple account have the old address. In trying to stop the hacks the password was very often changed and so I forgot it and cannot get into it to make changes. The address book and messages were actually taken out of that old address and so it had to be changed. I'm missing messages that are still going to that account. I can't even find where to change my Apple account so it gives the new address. Please help!