I had fraxel laser treatment under my eyes. I know have red and purple dots under my eyes. (photos)

Redness can last weeks to months after laser depending on how aggressive the treatment.  Steroids may help give improvement. I recommend following up with a cosmetic dermatologist for after care including a hydrating calming skin care protocol. Best, Dr. Emer

There is no need to be concerned. This is superficial bruising and it will go away within a week or so. You can use not so heavy make up to cover it up. You can use topical creams, gels and oil to speed up healing process. Arnica oil or gel is good for this. Good luck!
 

Some redness can be normal after Fraxel® laser skin resurfacing but, as you appear to be quite concerned about the spots which have appeared, a follow-up appointment may help to put your mind at rest. With regards to speeding up the healing, all you should be doing is following the instructions which were given to you by your plastic surgeon before the procedure was carried out. Additional advice may be provided once your skin has been examined in person.

Thank you for your questions and photos. Looks like you have some petechia that have developed under your eyes. These are superficial bruising from your capillaries leaking due to the laser treatment. These will resolve on their own within a week and are of no concern. You can use arnica, which is an otc gel on the area which can help resolve bruising quicker. 

Petechia are very small bruises caused by specks of blood leaking under the skin. They should resolve in a few days or so. It is cause by the laser piercing small superficial vessels in the eyelid. It is of no consequence and should not be of any concern.

Thank you for your question and photos. The Fraxel laser works in conjunction with the body's natural healing. While the magic is happening beneath the surface, please avoid direct sunlight, wear sunblock every day, and moisturize. While you are healing, you may wear makeup. 
If you have swelling in the area, you can use some ice, or cooling gel eye mask. The dots are scabs and will heal in the same time it takes your body to heal from bruises or scrapes. 

Be patient, once you heal you will be glowing!