I am sorry to hear about Boogers.
My name is Rebecca. I am a veterinarian, and will do my best to help.
The first thing I would check are his teeth. Rabbits teeth grow constantly, and can become too long and need trimming.
You can't see the back teeth just looking in the mouth; bunnies have very long narrow mouths. I use an otoscope in the mouth to look at the molars, that is the only way to look at all the teeth. If there is something stuck between his teeth, that would be the only way to see it and remove it.
If the mouth is normal, then I would look in his ears for the reason for his shaking his head. But from your description, I agree, I think the problem is in his mouth.
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