Hi there ninaysabelr,
It sounds like your Apple ID works for other services but for iMessage and FaceTime the process just loops back to the beginning. I would start by quitting the Messages, FaceTime, and Settings apps:
iOS: Force an app to close
Double-click the Home button.
Swipe left or right until you have located the app you wish to close.
Swipe the app up to close it.
If that does not resolve the issue, then I would use the troubleshooting information in the following article:
If you get an error when trying to activate iMessage or FaceTime
Thank you for using Apple Support Communities.
Regards,
Sterling