i found out that my boyfriend is cheating on me and he hasn't apologized or shown any remorse. What to do?

Hello. I am really sorry that this has happened to you, with you seeing a message which was upsetting and then having your boyfriend not acknowledging this or apologizing for what happened. It sounds really upsetting and that you're concerned he may want to break up with you. I wonder if you have spoken to him about this worry that you have, and how this went when you tried to speak to him? I am also wondering if your boyfriend knew that you also saw the message from his cousin saying that his girlfriend came to their house. 

It sounds like having an open, honest conversation about how this has impacted you might be helpful. Sometimes stating that you are worried about something you saw and it has made you feel a certain way can begin a conversation. You can also say that as they haven't acknowledged or apologized for this you are worried that they may want to break up with you. 

These are things that can help to open up a conversation about the message and how you felt afterwards and to begin to think through with your boyfriend about how best to move forward with this, if this is what you want to do also.

It can be helpful to be curious about what is going on as we know that sometimes our minds jump to 'the worst scenario' (our brains do love to play tricks on us sometimes). I am not saying this is the case here for sure, it is just thinking about different possibilities with the question you asked.

Perhaps actually something else was meant by the cousins message instead of these messages meaning that your boyfriend wants to end the relationship with you. The only way we can find this out is by having the open conversations with others in our lives to 'check out' these worries. It can be scary to do this too, especially if we are worried that someone may want to end the relationship. It sounds like you're really thinking about how best to work through this and seeking support and guidance too by asking this question which is a really helpful step too.