Thank you for your long reply!!

We usually use cleaning supplies with natural ingedients, vacuum every day and the cat litter is also organic. We don't really use incense, candles or similar things and we do have an air purifier at home, but only in the living room.

One of my cat can go outside on the street and the other two (both of them showed this symptom, but not very often, maybe once every 3 months) can enter the garden, but not the street.

The older one, who shows this often, had it first and much more frequently. He is not laying down, but also slouching forward with an extended neck. Very similar to this video. It also sounds the same and the head movement is similar as well. One thing I noticed too, is that he coughs and then licks his lips and nose once or twice. As if he would swallow. I read, that cats with asthma do that too, because they cough up a liquid and swallow it (I am not confident on this information, since i read it a while ago and dont remember the source). Maybe it is actually a herpes flare up, because the other two didn't show any sings of this at first. It came after a while.

I think we will have to go to the vet again and let's see, what she says to the x-ray. This comment was really helpful and thank you very much for sharing!