I know this post is SUPER old, but I had an experience with this exact thing about a year ago, and I wanted to share how I treated it incase anyone needs another solution! We took the more “involved” route since my gal’s neck was getting pretty bad, side note: how odd that this happens in so many people’s 3 week old chicks! My gal was 3 weeks when this happened as well.
Basically, we took her to a vet, they drained one, and left the other 2 lumps alone, they wrapped her neck w/ that sticky vet wrap, and used some kind of treatment underneath, although I’m not sure what exactly it was. We gave her antibiotics twice daily, and changed the vet wrap around her neck once daily. We would occasionally spray vetericyn on the wound. She was kept isolated inside until it fully healed because we think it was caused by others pecking her. She made a complete recovery, and she’s doing great! Although I don’t think you need to take as involved a route as I did, I would highly recommend the vet wrap around the neck to keep the chicken from scratching at the wound, as well as to keep other chickens from pecking the wound, permitted you don’t want to keep your chick inside for about a month or 2, and antibiotics if you can get your hands on some. Spray with vetericyn, as well as bluekote, especially the bluekote if they’re going to stay outside/with other chickens!
I hope this was able to help someone who’s dealing with this problem, it was very scary and stressful for me when I was dealing with it because I couldn’t find any information online about it since I didn’t know what to search. I’ve inserted some photos of her neck before, and after the treatment!