How is he today? Any changes?
I don't think the shaking was related to choke, you don't seem to either. That sounds like he was cold. I recommend feeding more hay as the digestion of hay creates an enormous amount of heat and will help keep him warm. It doesn't have to be good hay, just low in dust for his allergies.
Have you tried soaking the hay to remove the dust? This might help his allergies a ton. If soaked under 20 min(I think, it's been a while since I read that study) it won't change the nutrient levels in the hay at all.
Usually a horse won't continue to eat if he's choking, I really don't think this is choke. He may have inhaled some hay dust in his nose and snorted it back out, and he may have a cold or allergies.
The questions you need to ask are:
-Is he eating normally?
-Is he drinking normally?
-Is he pooping normal stools and a normal amount?
-Does he have a fever?
Get back to us on how he's doing.