My 3 month old appears tobe having severe cramping he's been between sleep and screaming since 4pm now 3am and they are persisting do i go to hospital?

Yes: Abdominal cramps (called colic) in infants is common and seldom serious but this is an unusually long time to persist. While it may not be serious it could be a serious condition called intussusception. I would be particularly concerned if he recently had the rotavirus vaccine, which significantly increases the risk of inussusception, a reason I am not a big fan of that vaccine.