Am I entitled to be compensated in NY State and how is it figured?

NY State Restaurant. Eating dinner with 3 other people on a Saturday night. Told waitress I was allergic to all nuts before I ordered by meal. Ordered soup off of the specials menu that listed ingredients...except pine nuts. Ate the soup not knowing pine nuts were in it. Called waitress over and gave her the assumed nuts that were still in the soup to check with the kitchen. She came back and confirmed, via the chef, they were pine nuts. She also confirmed she gave the kitchen the allergy note. The manager came over to apologize and said the chef and his line missed the note as well as recognized they didn't list pine nuts as an ingredient on the menu when they should have. I ended up in the hospital...epinephrine, IV, etc... Basically, took me about 18 hours to feel normal. $4,100 Emergency Department (ED) bill....however, I do have insurance. ED notes confirm a reaction. No loss time away from work.