I haven't read every post but I have an idea. What about those worms that bore into rabbits. I've known cats to get them too. They eat their way through the animal leaving infection behind. That could make them shake their heads and not be able to eat. I've always seen these worms around the neck area. We call them Wolf worms, not sure of the spelling of that but thats how we say it. And i'm not sure if thats what they are really called. What we did to get rid of them was very painful but it worked for those not to far gone. We squeezed the worm towards the hole they made to get in under the skin. Pulled them out with tweezers. It stinks to high heavens, sour smell. Boiled out with peroxide and packed with neosporin.
I don't now if this is what it is, as I said, I didn't read all they way through. I just wantd to post this before I forgot my idea. Bad memory.