I think that problems in my new relationship make me think that it was my fault that I got cheated on.
You were cheated on in your previous relationship, so is that the reason you think that in your new relationship?
Yes, I still think a lot about my ex.
If you got cheated on by your ex, that wasn't your fault. Don't take responsibility for other people's choices.
But my heart is making me blame myself for everything.
Don't blame yourself, instead try to move on and find someone who appreciates you so that you can find happiness again.