Hi, I googled mycoplasma synovial and it looks like the preferred treatment is tylosin, followed by tetracycline. I guess you could do both since we're not sure what she has and those two cover a wide range. Looks like chewy.com and Tractor Supply both carry tylosin powder OTC. You can give her...
It sounds like she has some form of farm pathogen. Oregano oil is a good place to start, it has strong antiviral and antibacterial properties. Amazon has oregano oil for poultry.
If the sneezing gets worse after she goes outside, maybe she's allergic to something in the air.
I didn't see anything about a leg issue in the initial post? Marek's can cause gradual paralysis.
Mycoplasma can cause pneumonia like symptoms and also nervous system issue.
Have you tried some...