What treatments can help reduce this under eye purple discoloration? (Photo)

You are seeing the muscle through the very thin skin here.  You are a little hollow, so some filler such as belotero or restylane will help with the color.    

You may want to talk to a doctor to see if fillers may work for you. Maybe talk to them about Belotero, or what other fillers they recommend. This is something that you do not need surgery for .

What you are seeing is the thin lower eyelid skin overlying the red orbicularis oculi muscle.  Eye concealers are like liquid photoshop.  The place reflective make up on the eyelid skin and this allows light incident onto the eyelid skin to bounce off.  This is probably the simplest fix for this issue.  Alternatively, a small amount of under eye filler will provide some volume and this can also help.

The good news is that what you are seeing and describing is pretty much normal, given your tissue type; the bad news is that there really isn't a definitive treatment for it.  The skin of the eyelids is the thinnest skin on the body, and it is very translucent.  In addition to this, there really is no fat immediately under the eyelid skin between it and the underlying muscle like there is everywhere else in the body.  This allows the intense purplish-reddish-brown color from the underlying muscle to show through this very thin, translucent skin.  In some people, typically from Asian or Mediterranean races, there can also be melanin, or brown, pigment in the skin here, but this doesn't seem to be the case with you.   As you said, you are of fair complexion, thus your skin lacks pigment of its own, making it more translucent, and thus allowing the underlying muscle pigment to be more noticeable.  There is no good treatment like lasers or anything injectable which will help this, as it really is just the natural state of affairs with your tissues.  Sometimes the appearance of the pigment can be magnified by shadowing caused by contour depressions and hollow areas around the eyes, and these can be camouflaged with filler injections, but short of this, there is no injectable treatment that I know of that will directly affect the pigment issue we are discussing.  The best, and safest, strategy for dealing with this really is to find a good concealer which will blend well with your skin tone and cover the areas of the most intense pigment.  At your age, my recommendation is to be as conservative as you can with your treatment options, especially at first while you are still figuring out what will work.  Good luck.