She may have been in a cage with that many budgies because she had no choice...she may not have liked it then either.
And the green cheeked are quite a bit bigger....it just sounds like there might be a crowding issue irrespective of the cage size ( which I am hoping is quite large given that you've got 10 birds in there!!!)
When you brought home the new budgie, did you isolate her from the others before you put her in with them? If she came from a pet store ( not that breeders are exempt but petstores are worse) she should have been kept on her own anyway for several weeks to make sure that she didn't pass any unknown illnesses on to your other budgies. Given their current living situation, I would say that putting her in a separate cage and going to the vet are now imperative, given her sneezing.