Here are some other threads about lumps on the neck in turkeys:
https://www.backyardchickens.com/threads/lump-on-turkens-neck.303963/
https://www.backyardchickens.com/threads/naked-neck-chicken-has-two-bumps-on-neck.1308626/
I missed the part about giving antibiotics. I would stop those, since your other chickens do not need those. Mareks or avian leukosis virus can cause tumors. You could try lancing on of the lesions to see if there is just blood and tissue, or any pus or ingrown feather inside. But I would...
I haven’t seen that before. I would have guessed it might be an ingrown feather cyst if it was in a feathered area. It must be a cyst or tumor, but it seems to have developed at a very young age to have been so large at 3 weeks old. Have you every had a virus in your flock such as avian leukosis...