Yes, it looks like a cockerel next to that other chick. Also the larger red comb. But the saddle feathers seem too wide and rounded to me. I guess you will need to wait to hear the first crow or discover the first egg.
Keep up the cold compresses under the wings for a while longer. The feathers...
That appears to be a pullet to me. At that age, with a Brahma, I doubt it's an egg issue as they don't mature until close to nine or ten months.
Did this pullet come from hatching within your flock? A private farm? Hatchery? The clicking sound when she breathes can be from a respiratory...