I'd hold onto it for a little longer just to be sure. Adding a week old chick to 3 week old chicks could be problematic as the older ones will typically bully the younger. I recently added 3 week old chicks in with 5 week old chicks. For the most part it was peaceful, but the older chicks noticed that one of the younger pullets had a wound on her head and practically cannibalized the little thing. They literally at all the flesh off of her head and neck. I've had her in isolation healing ever since. She's making a remarkable recovery but shows absolutely no interest in returning to her flock.
can't say i blame her. i had an adult sebright get pecked to the skull buy chickens who were several months from being a year old. but i separated her until i got rid of the younger birds. then put her back in with my other sebright and my japanese bantam roo. she ruled the roost then bare skull and all. the skin has grown back now but she still has a bald patch. really hope the feathers grow back.