Do things get brighter as they travel faster and if so what would the general equation to model that be? I'd like to preface this by saying that I am not talking about glowing caused by the heat generated from air resistance. Instead lets just say that the hypothetical object we're talking about it in a perfect vacuum.
This question was inspired by the idea that a car is hit by more rain when it is moving than when it's stationary. Does this concept apply to photons?
In other words, do things get hit by more light and therefore reflect more light when they move at higher rates of speed? why or why not? If they do then I'd love to see a general equation for a given object (let's say a sphere to make it simple).
 A: No, they do necessarily get hit by more photons, for the simple reason that you have to start by defining what light sources are involved. And you also have to define "brighter," which I'm guessing you mean "more photons per second are reflected into my eyeball."
So let's look at two cases. First, like with rain, assume illumination perpendicular to direction of travel.  You end up with fewer photons being reflected towards you the faster it moves, just like you running thru the rain.
Second, suppose you aim a flashlight directly at the object.  Then (perfect collimation), all the photons are reflected back at you.  If the object is stationary, then all the photons arrive in a time period equal to the length of time the flashlight is turned on - a "pulse width" .  If the object is moving towards you, the apparent pulse-width is reduced by the distance the object moves during the pulse-width time. (there's also Doppler frequency shifting but I don't think that's what you are asking).  So in this case, I believe you'll see a shorter and thus brighter (photons/second) reflection.
