burst into tears
This describes someone suddenly starting to cry loudly.
it breaks my heart to do this, but...
You are going to do something harmful to someone. You want to show that you are sorry and you don't want to do it, but you feel that you have to do it.
You are someone's boss and are extremely angry with them. You want to fire them in a very dramatic and angry way.
I think she's cheating on me.
You are talking to a friend about your wife or girlfriend. You want to say that you think she may have another lover.
My girlfriend and I broke up.
You are talking to a friend and telling them that you are no longer together with the person who used to be your girlfriend. You are suggesting that the break-up was agreed on by both people.