Sounds like because you have a similar reaction in your throat to nuts and peanuts, you should consider the coconut reaction an allergic one. Coconut oil surely has some type of proteins left it in because we're all generally after high quality, unrefined coconut oils in paleo land. I think the addition to coconut oil to our diets, while great for most, also identifies existing allergies in some who otherwise might never have detected an allergy to coconut on the SAD.
Many people w/peanut allergy can technically eat peanut oil because it is highly refined supposedly with little or no proteins left in it... however, to someone severely allergic it is not worth the risk. Coconuts are considered tree nuts, which would explain the similar reaction.
Don't underestimate any reaction that makes your throat sore or itch. It's a hop, skip and a jump away from full-blown anaphylaxis, which is life threatening. I suggest anyone who gets a sore throat or itchiness in the mouth/throat gets an EpiPen because reactions are not predictable. Stress or weakened immune systems due to colds, illness, etc. can significantly increase the likelihood of a life threatening reaction. There's just no telling what will trigger a reaction into escalating into something very scary, and it's just not worth the risk.