Time cannot be sped up or slowed down for a single person. It is only when you compare two different frames that are in different conditions that the effect arises. Each observer sees time pass at the exact same rate for themselves as they always have.
If you leave a large gravity well and return later on, as long as you haven't been at very high speeds compared to your point of origin, you will have had more time pass than it did. Basically at least. It's a little more complicated than that of course.
Edit: I want to be sure you understand that time has not been changed for YOU. Your watch will always tick at the exact same rate that it always had, when viewed by you, no matter if you are at high velocities near the speed of light, or at a dead stop in empty space.