Trouble With E-Mail

My original Xfinity e-mail was hacked and compromised. I thought I closed the account and made a new Xfinity e-mail account. I have three other e-mail accounts (Apple, Google and Yahoo). For some reason, when somebody sends an e-mail to my Apple "me" e-mail account it also goes to my old Comcast e-mail account and I get the error message that the e-mail cannot be delivered and it references the old Xfinity e-mail account that I closed. How can I stop this behavior ? An example is somebody sends an e-mail to my [Edited: "Personal Information"] account and then the error generated is a long message saying the e-mail cannot be delivered and it references my old Xfinity e-mail account which I thought I deleted. My old account was [Edited: "Personal Information"] and my new Xfinity address is [Edited: "Personal Information"]. My Apple e-mail is [Edited: "Personal Information"]. Any help would be appreciated in actually getting rid of the old e-mail because in my profile and user settings my old Xfinity e-mail is still there (not the new one).