If she’s very sleepy while drinking the milk, she may not be controlling the speed of drinking well and hence choke on the milk. Actually, for your consideration, it might be a good time to stop night feeds since she’s already 2 years old:) let her drink more before bed time, then let her sleep through the night. Tell her there will be no more milk at night so she can sleep better:)
Maybe cn try alter milk time to be before sleeping. When you see her eyes sleepy, give milk. Or maybe reduce the milk when she wakes up. Maybe her waking up at nite is jz out of habit and wanting to "feel" like shes drinking something, unless her last feeding was very long, then needa give her appropriate amt.
my kids have sensitive ear nose throat so i stopped night feeds around 2yo.
Maybe try reducing the amount of milk?