Could it be molting. Birds molt at different times of the year. If not Per Understanding Molting if your bird is losing feathers at a time other than its regular molting period, there may be a problem. read more
PBFD attacks the immune system and the cells responsible for feathers and beaks, and will often show up when birds molt. If your bird’s feathers grow back abnormally, are missing, or are loose immediately after molting, you should immediately contact your veterinarian and make sure that it isn’t sick. read more
As to the bites on you, the lice that afflict birds do not live on people. Our pigeons have gotten feather lice from time to time but I've never seen one on me, let alone been bitten by one. Losing feathers around the head and neck and even having bald patches is common during the molt. read more
Pigeons will lose a lot of feathers if they are caught by predators or hit by a car, most often those from the back, the tail and/or the flight feathers from the wings (these are the long ones at the end of the wings). read more