If you were travelling at the speed of light you would have no mass which you don't. So firstly you can't travel at the speed of light, but theoretically you can travel close to it. So in this moving reference frame your time doesn't stop it continues, but to an observer in a stationary refernce frame your time slows down(time dialation)

Also the speed of light is the same in all reference frames(moving or stationary), according to one of eisteins posulates in his special theory of relativity.