I had Laser Vein Removal on my legs and they are now scarred beyond imagination. Did I get burned by the laser? (photo)

It is hard to tell from the pictures if you have hyperpigmentation or laser burns.  A laser burn would occur within several days of the treatment and hyperpigmentation would occur later.  Either way it will take time to heal and for now topical treatment with a hydrocortisone cream may help.  If it is a laser burn, sometimes silvadene will help topically.  Also, an over the counter item call Bag Baum has hydroquinolone in it and may be beneficial.  You should certainly follow up with your treating physician.

Initially, the laser treatments can be inflamed and tender to the touch with hyperpigmentation. We recommend the use of topical steroids like 1% hydrocortisone which you can buy over the counter. Use it directly on the areas treated several times a day and wear compression stockings for at least 4 weeks - we recommend 3 months. You can (and we recommend very highly) the use of topical creams like VenoQuin FADE and VenoLucent on the treated areas to help fade away the hyperpigmentation. I cannot tell from the pictures if there are burnt areas and they should heal - see your treating physician if you continue to have this pigmentation. 

Without examining you I cannot tell for sure, but hyperpigmentation with laser vein treatment on the legs is very, very common.  You should  be putting sunscreen on your legs and should have the doctor who treated you take a look at your legs. It might need to be treated.