Although it is really worrying when you introduce a new pup, I just thought I'd recount how Bella was with Zorro (and they are now best buddies - he's 4.5 months old):
Initially she was quite scared by him but this quickly changed into her doing lots of growling, grumbling and pinning him down. The noises she made were terrible and it did often sound like she was trying to kill him. He in response screamed blue murder. To begin with we were quite worried but then we'd check him over and 99% of the time he didn't even have any of her saliva on him so she was clearly not actually touching him. I'd done quite a bit of reading on here about introducing a new pup and the fact that the existing dog will want to lay down the law. We just let Bella get on with it - she clearly knows what the rules are and he clearly needed to be taught. After a couple of day sit was obvious that she had a scale of punishments to fit the crimes, so to speak, ranging from just a low, warning grumble to the doggie equivalent of six of the best, chasing him and then once she got him in a corner, flipping him swiftly onto his back (with much snarling) and standing over him briefly before releasing him. He would always scream his head off during this but often he had actually been warned 3 or 4 times before Bella resorted to this. For certain things she went straight to this serious telling off, eg if he took a toy she thought was in her possession or approached her when she had a hide chew or something.
She also snapped at him if she was heading to us for a pet and he came to join in, or if she was being petted and he tried to get in there, or if any visitors came and she was still saying hello to them.
We ignored all her growling and tellings off but really praised her for times when she was being nice to him, eg letting him settle down within feet of her without grumbling or letting him walk close beside her.
The other thing we did, which I think really helped, was to make sure she got time out from him - she was allowed to go upstairs and have quiet time, she got taken for walks without him and got taken into different rooms for training and play sessions and general cuddles and attention without the pupster interfering.
She spent 3 days really telling him off alot and then on day 4 discovered she could play with him and that changed things alot. They now get on famously although he is still very young and just starting to lose his puppy license so gets told off for various things and sometimes still gets really snapped at, but again, we let Bella get on with this, she's teaching him right from wrong in doggie terms and she knows far better than we do.
I'd say definitely don't tell Sophie off for growling at him as this is her giving him warnings - if you watch them carefully you might well see that Sophie is giving the pup these warnings BEFORE going into snapping and snarling mode. This is certainly true with Bella, you can see Zorro just being cheeky and pushing it despite her warnings and he then inevitably ends up pinned to the floor squealing like a stuck pig, but in my view he's kinda asked for it!
I really hope things start to settle down for you - just remember it's a HUGE change for Sophie so she needs time to adjust, and the pup does need to be told by her what it can or can't do. Give Sophie plenty of time on her own with you doing the things you've always done with her and lots of praise any time she is being okay with the pup.
