Have you never asked yourself why a 37 year old would be interested in dating a 23 year old? Someone who is closer to his son's age than you?

Let me tell you, decent people who prioritise their own kids simply don't do it. Your bf knows how mature the average 20something person is..... and given he has a son this age, his choice in partner, and the rushed timeline is a flag.

In march I moved in with him

What was the rush about?

, and I don't know what he's going to say when he finds out about my relationship with his dad, I don't even know how to tell him, should I tell him or should his dad tell him?

Your friend is going to be shocked, and grossed out. Your friendship will most likely be over, no matter who'll tell him.