Dry eyes following blepharoplasty are usually due to more of the eye being exposed leading to evaporative loss. With age the amount of tear production also decreases as well as from certain procedures such as a Lasik surgery. It is highly doubtful that your lacrimal gland was injured if the surgery was perfomed by a board certified plastic, ocuolplastic, ENT, or opthalmologist.
Fortunately there are many options to relieve your sypmtoms. See your opthalmologist for recommendations.
Since there are three glands that provide tears in different concentrations, and it is very hard to injure even one of these glands, much less two (one on each side), you probably have a lack of closure and tear evaporation problem. You can get a dry eye test at your eye doctor to determine tear production. At night when sleeping ask someone if you close your eyes completely, this will be a clue. There are treatments to cure your problem