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.