I had two Speckled Sussex with something very similar. The had yellow nasal discharge during the first round and just slowly got better in quarantine. About a year later it returned but less severe and without drainage. This time I took one to the vet and did a course of Doxy as you are. It did nothing. I ended up putting VetRx under her wings and putting a heat lamp on her at night and she recovered “fully” meaning she never exhibited symptoms again but I always considered those two birds carriers of something. The reason I mention this is that whatever it was none of my other birds ever got it. There is a possibility that the situation my Sussex were in when I got them was responsible for their respiratory issues. Their previous run was devoid of vegetation, shade and dirt. It was literally fine desert sand (not brought in, just base substrate) so they were breathing it in all day in the summer and probably any time the wind kicked up or they scratched in it. I think it did permanent damage. Edited to say: she also had a purplish comb each time.