As I understand this If I am traveling the speed of light holding a mirror in front of my face I would not be able to see anything, correct?
Cannot be answered for two reasons.
First, nothing of mass that we know of can move at or faster than the speed of light.
Because of the theory of relativity and associated conclusions, we cannot give infinite energy to a particle of mass to move it at the speed of light. Light itself is composed of photons (particles without mass.) They have momentum so they can interact with matter, but we cannot force enough energy into something of mass to cross that barrier. This is backed up by the tested theory that accelerated electrons became heavier up until the point of the speed of light where it was impossible to force them to go faster. It was then mathematical conclusion that the faster something of mass travels the more massive it gets and the more time slows. At the speed of light then time would stop, and by consequence so would speed. The natural conclusion is nothing of mass can travel faster than the speed of light. Einstein tended to agree.
So all you can really do even by theory is get really really close to that barrier, but with real consequence by these theories.
Second, because of the above all we can do is theorize what the conditions would be like for getting right up to the point of the speed of light holding a mirror.
Up to the point of the speed of light, then we are left with a two constants that must be met to ensure you would see your reflection in the mirror regardless of being at any speed or at complete rest. One, that the distance between yourself and the mirror is at a constant. Two, the speed in which both are traveling is in the exact same direction and also is at a constant. Acceleration and deceleration in these conditions at these theoretical speeds presents physics based calculation problems in a multitude of ways.
Example. If both you and the mirror were going at the speed of sound, then there is no difference in what you would see when compared to being at a stop. It might look very different but the reflection speed is itself unchanged. The same is true getting right up to the point of the speed of light, in theory, as the constants are that speed and that distance between you and the mirror. This is all based on the Theory of Relativity. The rules of physics have to exist in all conditions, in this case the same frames of reference no matter moving at some speed or at a point of rest. The frames of reference are you and the mirror. Assuming neither acceleration or deceleration, momentum changes, directions, resistance, etc. then light (thus reflection) work as usual. Again, light has no mass and is not subject to the same forces that govern say... sound and travel (think the Doppler effect on sound emitting from objects in motion vs. an object at rest.) And since sound is nothing more than a pressure wave through a medium of particles, we have different physics conclusions for dealing with sound in motion vs. light in motion.
You may think that moving faster and faster somehow diminishes what is seen in the mirror, however so long as the distance between your face and the mirror is the same it should not matter how fast both up to the point of the speed of light. It is not very practical to even try this, and even comical to think about what that reflection would look like, by theory we have enough mathematical calculation to determine these conclusions from the Theory of Relativity.
Now, with the compression and collisions of space theories from Quantum Sciences we can have a lot of fun with this subject. But, still nothing of mass actually travels faster than light in this universe... we just compress the confines of this universe to force objects of mass into unrealistic and totally theoretical consequences, including applied speeds for objects of mass over visually measurable speeds.