That sure looks to me like breeding injuries. Can you get a picture of the other one's chest so we can help you be sure whether it's not a boy? Sometimes even boys will have some speckles on their chest, but they'll have a rustier coloration. They also tend to be smaller (in general--this varies by individual). How do you know which one is laying?
I love that your birds are on grass! Yay! I'm concerned about the enclosure's security, though--do you have a perimeter fence around your property to keep out raccoons and foxes and so on? Or a large guardian dog to deter them? If not, a raccoon can rip right through the chicken wire or even just reach through with a dexterous little hand and grab one. I have had a raccoon grab a quail's toe through a 1/4" opening in a brooder floor and rip off the entire leg, also had a raccoon reach through chain link and rip off a duck's head. I'm not telling you that to scare you, but because I didn't take the risk seriously until it happened to me, so I'm hoping others can learn from my bad experiences. Also, some predators will climb (and hawks can fly and can easily take a quail, so I always make sure the top of the enclosure is covered.
Also, I'm wondering where your girl could have boinked her head--it doesn't look like there's much in the way of room for that. And mine don't "boink" in a large enclosure anyway--only when they're stressed.
To answer some questions, unless the flies are unbearably thick, they are not a problem. They'll lay eggs in an open wound (which is what the Blue Kote is designed to prevent), but not just in the feathers. Well, some kinds of flies lay eggs on horse legs, and the eggs are called bots and you have to take them off because the maggots are a danger to the horse... but I've never heard of this for birds. You can get Blue Kote at the feed store and neosporin at any old pharmacy. I second the recommendation to ask your pharmacist to point you to a formulation without painkiller. The store brand version of neosporin will work just fine (it's just an antibiotic ointment). But actually, if what you have there is a breeding injury and no open wound, it doesn't need either of those things. It just needs more females in the pen.
Good luck!