SIM not associated with my Cell Phone number

Go to Settings/Phone. Note your phone number at the top. That is the number that Messages uses for SMS and MMS. If it doesn’t match the number from your SIM you can correct it; that field can be edited. It defaults to the first number your phone had when you activated it, but it is not automatically updated when you get a new number.

Planter279 wrote:

iMessages will only sent using my email address, not my phone number.

Have you gone to Settings>Apps>Messages>Send & Receive and made sure that everything is checked in the top section?

It seems that my cell number is not associated with my SIM.

That seems unlikely. If your number was not associated with your SIM, you wouldn't be able to make or receive calls. Your carrier knows which phone number is associated with your mobile number by using the SIM.