How long will it take to correct my "vampire teeth"? (Photo)

Looking at your photos, you have a severe space deficiency on the upper jaw and as a result, the canines are locked out of the alignment. You need to find a good orthodontist to treat you. You many need to take some teeth out in the back to align upper jaw properly without compromising your bite.

I find it hard to believe that this is a result of a good orthodontic treatment but failure to wear retainers.  I see too much crowding to believe that the treatment was done correctly.  Attempting to treat everybody without extractions can lead to very unstable final results....get a second opinion..don't go back to the first doctor until you do