Chances are that the URI she contracted was viral (the more common feline URI's are), so all the antibiotic was doing was preventing a secondary bacterial infection from occurring while her immune system was busy battling the virus. Antibiotics, of course, have no action against a virus.
Just so you know, the most common URI - herpesvirus - is incurable, and almost all cats carry it. In most cats, herpes lies dormant most of the time. It can, however, flare-up into an active infection when a cat is stressed, immuno-compromised, or in direct contact with another cat with an active herpes infection. It's generally not a big deal, but it is highly contagious in the active state, and it can be a real nuisance in a shelter setting where one cat with a flare-up can trigger flare-ups throughout the feline population. Anyway, just wanted to let you know that you may not have seen the last of the URI's in your new girl. If it is herpes, which is likely, you may see it again if and when something triggers it to flare-up again in your girl. Like I said, more a nuisance than anything else.
Laurie