If someone is holding a photon light clock and they accelerate either up or down the photon would bounce quicker thus creating the appearance of the clock being fast from the point of view of the observer. Is this true?

accelerate or 'is moving'? show us some math. how do you calculate that it would bounce quicker?

If someone holding a light clock accelerates to a significant percentage of c, an observer in a relative rest frame will see the clock (and indeed time itself) moving more slowly for the person traveling at the velocity.

For a moving clock, the photon reaches one mirror faster, but the other mirror more slowly (the photon has to travel a greater distance) as measured by the observer in the other frame. Net effect is it runs slow, according to that observer.