Of course you're going to need to a hands on exam and labwork to appropriately diagnose this problem, but it could be any one of a number of bacterial infections.
Pasteurella Anatipestifer (Riemerella Anatipestifer Infection; Infectious Serositis) is a bacterial disease that might also be called ‘New Duck Disease’. There will be lethargy, loose stools/diarrhea, lack of coordination, head shaking/twisted neck, falling to their backs and leg kicking.
If caught very early there is a chance of management with antibiotics (prescribed, not self administered). Vaccinations are available and strongly suggested.
(Sulfadimethoxine-ormetoprim, Penicillin, Enrofloxacin .04-.08%)
Torticollis (wry neck) may occur in birds infected with Pasteurella bacterial infection, also known as Fowl Cholera.
A bird may be a chronic carrier, living with one or multiple symptoms; however, many birds that are infected with this bacteria progress rapidly with a high mortality rate.
Symptoms include (but not all need to be present): Lethargy, going off food/water, discharge from the mouth (often described as salivating or drooling), rapid breathing, fever (feet will be extremely warm), conjunctivitis (red, swollen, itchy eyes) and localized infections.
When the middle ear, cranial bones or meninges are infected, ‘wry neck’ (Torticollis) is seen.
Treatments include antibiotics such as Sulfonamides or in some cases, Penicillin. Be sure you have an experienced vet since Sulfas have toxic levels.
Other bacterial infections that may cause similar symptoms are:
Chlamydia, mycobacteria, salmonella, yersinia and others.
Tests should include sampling (and culture) of the nares (nostrils), oral cavity, cloaca,
etc., but if the vet isn’t knowledgeable about the normal flora in the bird species they are
examining, the results may not mean much. Inexperienced vets will find that the culture
grows something and often base their diagnosis on what they know of mammals.
It does appear you've caught this early - you're doing a very good job