My Newly Rescued Dog, Age 3, Had A Lot Of

My newly rescued dog, age 3, had a lot of snorting and sneezing. The vet scoped her, and said her nasal passages were extremely raw and swollen. She put the dog on doxycycline for a while, then on the return visit, gave her a shot of steroids and prescribed Zyrtac daily. She is definitely better, but I can still HEAR whenever she exhales through her nose, and one nostril is a little runny. (She is also on a diet that is free of anything that could contribute.) Is that just something she'll have to live with? A local pet pharmacy suggested chlorpheniramine maleate, but that looks like the side effects are unpleasant. What are your thoughts?