As you can see, the swelling is pretty extreme but I can see little black dots in some area under the skin.I've dealt with feather cysts a couple of times. I was able to see the ingrown feather each time. They were just under the surface of the skin, and I was able to just barely break the skin and release the follicle. It popped out like a jack-in-the-box. Then I sprayed the skin with Vetericyn and it was good to go.
Can you see a shadowy dark dot in the area of the swelling? First spray with Vetericyn or dab Betadine or alcohol on the cyst. Then take a sterilized razor blade or Exacto knife and make a very tiny, shallow cut where you see the shadow of the follicle. Remember a chick's skin is very thin. You may need tweezers to give it a gentle tug to release it. Spray again with the Vetericyn or Betadine or smooth on some antibiotic ointment.