How do I solve issues with my iMessage?

My iPhone is sending iMessages to my iPhone when they are intended to send to another phone, and this person is not receiving my messages?

I was also wondering how do I get my phone to stop sending text messages to another iPhone? This recently started happening when one of my family members got a new iPhone, they have turned off their iMessage and I have made my own Apple Id account to solve this problem although this has not seemed to work.