You can't be allergic to any kind of insect because there is nothing on them that you could be allergic to. However, if that dragonfly has been flying around bees, butterflies, or flowers, it may have pollen of dander clinging to it, and you may have an allergic reaction to that.
my husband is allergic to fish, anything with fur (he still goes hunting... the cheesehead has to go to the emergency room afterward but OH well.... walnuts wasps bees canteloupe watermellon and anything that has to do with dishes or laundry :-)