In your Settings go to Messages> Send & Receive and you should be able to set your preferences from there. Go to the "Start New Conversations From:" section and set your phone number to be the default.
If your phone number does not appear, turn FaceTime off and on. Phone number should show up
I had a similar problem, with the culprit being that iCloud got confused, and continued to send text messages as iMessages, so that my new phone (non-iphone) never got them.
Turns out, in order to turn off iMessages settings, you must disable iMessage EVERYWHERE. If you turn off iMessages on a phone, and leave it on your iPad, it won't reset (this was my issue).
So, I suggest you try this: iDevices (all of them): Settings>Messages. Turn off Messages. (on your iPhone, you can turn on sms message so at least you still get texts). On Macs, remove any accounts in iMessages by clicking '-' by them in the account preferences.
Make sure you have de-registered on ALL your devices. Give it an hour or so. Then create accounts on messages on the devices using your Apple ID. See if it works.
If this does not work, call AppleCare. I found that if you go to the AppleCare link in the website, it warns that it will charge you $$ per min for help if you don't have an AppleCare plan. Call the number anyway, agree to whatever. When I called, Apple did not charge me for the iMessages issue, as it is a known issue. (mine was slightly different, I will admit).
Best Answer
You need to review all the details of the Apple ID that is associated to your old phone. Make sure your phone number in particular isn't listed anywhere under the Apple ID that is currently in use on the old phone (you'll need to check this through apple.com to see the full detail, you won't see everything through the phone itself).
I had this happen re-using a phone from my wife, she started seeing my messages on some devices. Turns out I was using an Apple ID that had ended up with both her and my phone numbers listed under it. If you erased the phone but still had your SIM in it, your number could have ended up included in any new Apple ID created on the phone.