Your bird is suffering Trichomonas. In the pigeon world it's called Canker. It is a one celled protozoan that starts in the throat of the birds. It irritates it and mucus develops. The bird tries to clear it's throat, giving an odd bobble to the head (different from regurgitation when trying to feed a toy or other bird) and slings the head and the slim flys out. The tail tell sign is what you posted a pic of - a wet looking head that is dry, kind of like a punk hairdo.
To do nothing the "Trich" will multiply moving further down into the gut. The throat will continue to become more irritated and sore. The bird eventually will be unable to swallow food although you will think it is eating voraciously. If one carefully checks the feed dish one will notice the bird is only pulverizing the pellets and seed into a fine powder. The bird is starving to death. At this point treatment will not restore the bird to full robust health.
This is contagious to all birds in the same cage because they all feed each other. All bird need to be treated for this illness.
Some vets treat this with 250 mg Flagil tablets. It is a human antibiotic dissolved into a gallon of water. The bird is on this medicated water for 7 days, off for 7 days and back on for 7 days. Any step missed and the treatment will fail.
You can also go to Foy's Pegion Supply and look up Caker treatments. http://www.foyspigeonsupplies.com/
Many large budgie breeders keep Ronidazole (Ridzol) 10% power on hand to treat their birds.
I have also seen Flagyl Liquid there as well, but have not heard how well it works.