In my 37th week of pregnancy. Last week check up I was 50% effaced, 1 CM dilated. I've been having menstrual like cramping am I going to be early?

Not necessarily. You may be having the cramping as a result of the recent pelvic exam. Some women have a lot of cramping before they actually go into labor and others feel little until they really go into labor.
On time. 37 weeks isn't very early. This can occur and still carry til normal term. It depends on how much it changes in the next week, or if cramping becomes more severe and regular would go ahead and get checked out.