My son was asthmatic, has allergies, and used to get bronchitis. We own a nebulizer, inhalers, etc. When he was sick with regular bronchitis or a sinus infection we did antibiotics, steroids, breathing treatments and more.
What I always found, and it still holds true, is that the coughing is worse at night as the sinuses drain. No matter how much he propped up, he coughed. So to the medicine regime we always added a prescription cough medicine for night time, and I used Vicks Vapor Rub on his chest. These, combined, always helped his night time cough.
There was a time when he was just not shaking a head cold and bronchitis and we put him on a low dose antibiotic for 2 months. As bronchitis spiked the asthma, which irritated the bronchitis, which all became a vicious cycle. While I was not thrilled with the duration of the antibiotics his Dr was at a loss since regular, previously successful, medical routines were not working.
Now that he is a teen, when he gets a cold I can my tried and true symptom relief remedy of hot Jasmin tea with honey. Peppermint tea and honey also - both seem to soothe the cough.
As for the pets - We have always had them - cats and dogs - I sweep his room more often than the rest of the house, keep the cats mostly out of his room, and keep the animals off his bed. This helps limit his exposure to the dander.
My best advice, is patience. If she has had a sinus infection for this long, it will take longer than normal to clear it. The only other thing I can thing of is to ask the Dr to do a scan of the sinuses and make sure they are not impacted from the infection.
Best of luck to you. It is soo hard when they are sick. :(