Hi! I am so sorry to hear about your DD experience. I bet it was very scary for her. It could be a combo of things, the choking part being scary enough, but then having Daddy hit her and pick her up (if he reacted like I would have, it would not have been in a calm collective way) could have frightend her.
I would sit her down and discuss the situation, from beginning to end. How playing with food in our mouth is dangerous, and thats why she choked, (but if she sits at the table, its less likely to happen) choking is scary, how does she feel about it? Daddy was glad he was there to help, it scared him to see you choking, did he scare you by helping you?
And then ask her why shes not eating. Hopefully you can calm her fears by explaining what happend.
I did this at age 5 with candy, didnt touch candy for a long time! But it was for 2 reasons, the first I assocaited candy with choking, 2nd I assocaited the candy and choking with my dad picking me up in a frantic state tipping me upside down over a sink and hitting my back (at years old I thought it was very hard, but he probably wasn't hitting me as hard as I thought)
It wasn't until my parents did what I suggested here, that I even wanted to try candy again.
I hope this helps, or gives you some ideas. Best of luck!