I agree. If any of my guineas act funny, it's usually because they are injured. I've never had a guinea be sick. One guinea, let me get right up to it. He seemed alert and fussed when I went over to him, but let me pick him up. When that happened, I knew it was bad. What I didn't know, was that something (dog, coyote, etc) have basically eviscerated him from the vent outward.
I ended up putting him down. Check him all over. If he is shaking his head, be sure and check his neck, eyes, beak.
It could even be an older injury that is healing badly. I had a female that was in the same dog attack and she was skinned behind her wings to her tail. It healed wrong and gave her a hunchback and made her walk funny. She was vicious and I couldn't treat her, but the other guineas were taking care of her, protecting her, bringing her food, etc. That was one that I just let Nature take it's course, and hope for the best. If she had gotten really down, I'd have ended it, but she recovered and ended up having babies later.
The only other thing could be mites, but I doubt it. Check for them and dust if you see any. If you only see a few, then assume there are a lot. The head shake makes me think of mites. That, and the losing feathers, but I've never had any personal experience with them, so I don't really know.
Good luck!
Shelly