I should think the spray bottle you have will be just fine. If you are using the recommended 6.5 ounces of Oxine in 1 gallon of water, you can spritz right above her head and let the mist fall over her. (If you have a quart sprayer like I do, divide those amounts by four, of course.) Try this 2-3 times a day for a week and see how that works.
If it were me, I would also do the Oxine in her drinking water (1/8 teaspoon of Oxine per gallon of water) for 24 hours, and then change the water out completely and add a water-soluble probiotic the next day. (If you don't have that, you could do yogurt.) The Oxine will clean out remaining harmful bacteria in her throat and digestive tract, and the probiotic will help restore the beneficial bacteria. Not completely sure if that would help, but it surely can't hurt at this point.
(**I would wait until AFTER my round of antibiotics was finished before using the Oxine internally, though. I don't like mixing that stuff.**)