Lil is the sneezer right? NO point removing her since any pathogens are airborne and are already affecting the other rats. Once they have been in the same airspace QT is effectively over.
Do you have any idea what they were treating her with? Most Petsmarts treat with mild or useless antibiotics, that may hold a URI at bay but not cure it.
Rats will sneeze when they come into a new home, rapidfire sneezes but no other symptoms of illness and this passes within a week.
If there's other signs of illness you do have a sick rat. There are many combo's that work effectively on URI...baytril/doxy is the most common, I have used baytril/amoxicillin, baytril/zithromax, etc.
Don't worry about endoparasites at this point, the majority of rats have pin worms that don't affect them (or you) in the least.
You said Lil is going downhill? What are her symptoms?
Back to baby's fur. Diet can really affect coat and skin...what do you feed your rats? Is she a poor rex maybe?
Btw lice you will see but mites you will not (microscopic)...give all your rats a good feelover for ANY tiny scabs on their body. Lice prefer to start populating on the rumb, tailhead and back (you will see them crawling through the fur) and mites love the shoulders, neck, head, cheeks and chin. Dig your fingers into the fur deep, a stroke over the fur won't find those scabs.
Ectoparasites (parasites that live outside/on the body) usually will present on a compromised rat more than the others, so checking other rats for issues wont work. I took in 4 foster boys...1 had terrible mites scabs, 1 had classic mite scabs, 1 had just a few and the youngest boy had none...they ALL got treated with Revolution and were fine