Can you help me? My daughter is allergic...?

I live on Long Island, NY. There is a black flying insect that bit my daughter and she is highly allergic to. When the insect lands, the wings are in a triangular shape. They look lacey and black. I call it the 'triangle bug' lol but I dont know its name. Can anyone help? The one that bit her was small. I saw a larger one in the Hamptons and I was nervous that a larger one could really harm my daughter since the bite of a smaller one sent her to the emergency room. If anyone has any leads that would be great...thanks!