Dark Spots After Fraxel

Your genetic makeup greatly influences whether or not you'll be prone to hyperpigmentation after laser treatments. Those patients with South American, Mediterranean and Asian gene mixes (or mix of African or Native American) do tend to have more incidences of PIH (post inflammatory hyperpigmentation).
Alert your treating physician to this problem right away as I'm sure there will be some treatment he will prescribe. And be sure to wear sunblock as advised.
I have a few Questions for you and Cautions for others

Did your physician ask about your ancestry? If not, and you're anything except full Northern European, always inform your dermatologist of your mixed gene pool. Actually, your physician should always ask, even if you're the color of milk!
If you are of mixed ethnicity which includes darker skin, did you undergo any pre-treatment with a melanin suppression agent? This will sometimes prevent - or at least minimize - a hyperpigmentation response.
Were you advised of caution in your sun and heat exposure? Sun exposure, hot tubs, steam rooms, poolside and beachside days, golfing, even cooking...all these can trigger a melanin explosion following laser treatments and should be avoided.
If you are of mixed ethnicity and your physician knew this and gave you a pre-treat plan, did you opt out of following the pretreatment program? If you were advised and prescribed and chose to only partially follow a pretreatment program, then that lapse is part of the problem.

You may find that remedying your new hyperpigmentation requires much patience over months and a variety of corrective treatments which will likely include RX levels of hydroquinone. You'll need to adhere to the corrective treatment protocol (don't try doing the drug store fix as it probably won't be strong enough) and be dedicated to sunblock and hats.

It is difficult to know what happened and predict what will happen without seeing your skin and finding out a little more. Some people develop dark marks after they have any kind of inflammation in the skin; this is called post-inflammatory hyperpigmentation. This is more common in people with medium and darker skin tones. It can, however, happen in people with light skin who have a mixed genetic background. Rarely people can have darkening of the skin after Fraxel that can last for several weeks to months. Whether you have darkening in one spot or a large area it is probably not permanent. It should be manageable but may require patience..
Did you have Fraxel re:store or Fraxel re:pair? Fraxel re:pair is more aggressive and can cause more redness, which could in turn lead to more post-treatment skin darkening. Fraxel re:store can trigger acne breakouts and acne-like spots. You say that you had a red spot after you had Fraxel, this may have been an acne-like spot.
After Fraxel, your skin is more sensitive to the sunlight. If you had sun exposure, even if it seemed very minor, you may get a darkening of your skin. Also, if you had any skin irritation, tried to "help" along the peeling after Fraxel, or used any skin products that caused irritation you could get redness and darkening.
But it sounds like your dark spot is post-inflammatory hyperpigmentation. Talk to the physician who treated you. You need to discuss everything that has happened with your skin since your Fraxel and all of your post-Fraxel skin care in order to determine the cause of this spot and the best treatment.