But special relativity still applies. So you can only do this by traveling at nearly the speed of light away from or towards your target. Travelling this fast is a separate power with separate side effects, and you don't have it.
You can't actually change time, just your perception of time. Your muscles don't move any faster. If someone is throwing a punch at you and you slow down time, you can appreciate the fist moving at your face for an hour of your slowed-down time, but you still can't dodge the punch. If you speed up time, you still need to eat, sleep, and perform other bodily functions. So, instead of getting hungry every few hours, you get hungry in what feels like seconds. And, since you don't have super-speed, you need to slow time back down again so you can eat.
It might still be a power worth having, but it's not as awesome as it might seem at first.
Would your reaction time change? Maybe the neurons in your brain would be going at super speed, but maybe your peripheral nerves would still be slow. So, the time between hearing something and the signal getting to your brain would still take ages. Or, the light would hit your eyes, but it would be a long time before that was processed into a signal your ultra-fast brain could use.
You can't actually change time, just your perception of time.
If you can't perceive anything while time is frozen as a consequence of biological structure, then your "side-effect" is just complete nullification. You wouldn't be changing your perception of time at all. Not much of a side-effect.
If your brain and senses can act at super speed but everything else in your body acts in real time, you'd still have an advantage in reaction time as you would be able to recognize and initiate your first reaction near-instantly.