2 year old RIR hen, 4 lbs
standing alone head down
find her limber necked, head hanging with random bouts of shaking her head out of control.
Vet prescribed antibiotics for possible ear infection and gave her a 50% chance of survival. We also began syringe feeding
weekend of antibiotics and syringe feeding with no change
Her poo is white and green
exact baby parrot food mixed with her calvamox, water, milk for calcium, 5 drops totaling 45mg vitamin e and a pinch of crushed selenium tab 100mg, and 1/4 to 1\2 dropper (1ml) poly vi sol minus iron
The poor thing, she is not doing well, I'm so sorry

You vet prescribed antibiotics for a possible ear infection - does she have pus or anything crusty inside the ears?
In your photo - it's hard to tell with the eye closed, but is there pus in the eye, is the tissue around the eye puffy? Swelling of the ear and what is on her wattle, is it just dirt or is there a bad spot on it?
Does she have any respiratory symptoms?
Any plaques/lesions or canker inside the beak?
Where are you located in the world (state/country)?
I agree with @Eggcessive some of the symptoms you describe and in the video look like Wry Neck, but that is just a symptom - figuring out the cause would be key. Did you vet do any testing on the poop or a gram stain.
All you can do is try to keep her hydrated, tubing fluids if you need to. See if she improves with the course of prescribed antibiotics. Personally I would ditch the milk and selenium. Increase the vitamin E to 400iu and give a very small amount of polyvisol. The Katee baby bird feed is fine.
Since she is under vet care, you may need to re-consult with them to see if there are any contraindications of what you are giving along with the Clavamox or if there is any other testing they can perform.
I'm so sorry, I hope you see improvement soon, if not, then consider how much more time you will give her and make plans to end her suffering.