That's another great question that unlocks another incredibly strange point about reality.

You're only moving faster/slower through space/time to an outside observer. Your own rate of time and your own velocity through space will always feel centered on you, and it will always look like the rest of the universe that is slowing or accelerating.

And in fact, another mind-melty point behind relativity is that if you jump out of a 20th story window, there is no action that says you're falling, instead the action is saying that you have changed your velocity (or altered Earth's velocity in respect to your acceleration) and now the rest of the world is passing you very rapidly. It would feel like Earth and the building and everything else is wooshing past you while you stand still. And that's a correct perspective. It is rushing past you, you are sitting still in space. (The problem comes when that wall of asphalt and dirt swings past and doesn't miss you.)

If you fall into a black hole where spacetime is distorted as far as we can imagine, to you nothing will feel different (at first) you will see the whole universe seem to roll into a tight ball behind you and it will look like it's in rapid-motion if you pointed a telescope into it, you would see stars being born and galaxies fading and the entire future of the universe will rush past and you will hit the singularity at the death of the back hole, some billions and billions and of years into the future. If you could magically escape right before you get pulled apart, you would find the entire universe has died outside and all the stars have gone out.

Time passes more slowly for you than for an outside observer, e.g., if you are moving to some place, for someone on the outside, your journey could take decades, while for yourself only minutes pass.