I just took my chickens to the vet a few weeks back for something similar. The head shaking, scratching, and stretched out gaping mouth is caused by congestion. Whether that is caused by an upper respiratory infection --where you would not see anything coming from the nose or eyes, or if it is caused by mold.. I don't know your situation. But the symptoms are being caused by something else. In my case, I'm thinking we had something viral since it lasted so long. If you have wet litter, mold, excessive dust, etc..? Of course, I wouldn't rule out worms, lice, mites, etc. Always a good thing to worm them. I had hoped my situation was going to be that simple too. But after dusting mine, and checking for bugs, and worming... they were still no better days later. Fortunately, I only had three sick that I had isolated. They took Baytril for 5 days injection. (.25 cc) And then VetRX for another week after that. But after everyone suggesting the same things you are getting-- our symptoms did indeed end up being congestion. (what they had, we don't know) Vet said their lungs were clear, so it had to be an upper respiratory (sinus) congestion. No discharge, but lots of sneezing, yawning, and head shaking and scratching. I'd put the VetRX in their water to help. I'm really sorry about your birds, I hope they do alright.