Welcome to the forums!
I'm sorry one of your little chicks is displaying abnormal behaviour. I will start by asking some questions, if you don't mind.
This head shaking you mention, is it like trembling? Can you describe the head motion your chick makes, does the chick shakes the head sideways to the right and to the left as if it's saying no? Is the head motion done up and down?
Is it only the head that seems to shake and how is the rest of the chick's body?
If this chick is about 3 weeks old, by now it should be able to move well on the nest and walk. How is the rest of this chick's motor skills? Does the chick move around well like its siblings?
I have never had a chick to display such behaviour. I have however had adult budgies that have been sick and when they were vomiting they did shake their heads sideways (left and right) and seed shoot out of their beaks while vomiting.
Another possibility is that somehow your chick had head trauma and is suffering from neurological issues. While I never had a case nor seen it in person, your budgie can be a "stargazer", I know stargazing occurs soon while chicks are still in the nest and if this is the case, then vet assistance will be needed for proper diagnosis and treatment plan.
If your chick continues doing those strange head movements, it really is best to book an appointment at a specialized avian vet.
Best of luck with the little one and its siblings. I hope it's nothing serious and soon your little chick gets back to normal.