The first thing we need to know is if you two are using the same Apple ID?
Why are you using the same Apple ID? (If that is what you guys are doing)
The massive headache from all the issues of trying to use the same ID is not worth it. If its about being able to share songs and apps, you may want to get separate ID's and use Apple's family sharing.
Sharing Apple ID's is like trying to share the shame identity in life. Not only will things not fiction properly but you will lose out on things that make you, well you. You both will lose out on what makes up the amazing Apple user experience. Individuality.
If you are not using the same Apple ID then check to see if both your phone number and your ID/email are associated with your iMessages in settings. Then do the same on the other device. Then check the contact information on each device. Does the contact information card match the iMessages information on the other device.