Just to let you know, that the little friend has fully recovered from the illness. Not sure what worked, but here is what we did:

1) Changed food and bedding to other brands
2) Rubbed vaseline regularly every day for a week, later switched to the following:
3) Alcohol-free iodine following by some cream recommended by a vet specializing in cats.

within week illness stopped to progress, within two weeks recovery started, within month the illness went away.