VERY IMPORTANT If it is not eating properly it will get sicker. You will need to hand/force feed the bird so it gets adequate nutrition and is able to survive. You can use peas to hand feed (defrosted, drained and warmed)gently open beak, place on back of tongue, allow bird to swallow (close beak) and repeat about 15 times. I would also give this bird a calcium/D3 supplement.

This may be neurological or trauma or something else. Has the bird flown into anything? What do poops look like? Is the keel/breast bone sharp?

It would be best to take the bird to a qualified avian vet.

 

I got a pigeon last year with wobbly head like that...he was diagnosed with paratyphoid/PMV based on symptoms. Are the droppings diarrheish or with bad smell..
If the droppings are watery, I would suggest to start him on an antibiotic like baytril, and a canker medication like metronidazole.
Hand feed him peas/seeds till his crop feels mushy, and then wait for another 3-5 hours till the crop has emptied, before the next feeding. You can feed him 2-4 times a day based on how fast his crop empties. To give water, dip the tip of beak (not the nostrils) into a little water taken in a bowl. He will drink on his own if thirsty...