Hi Suzanne, welcome.
I too would be hesitant with using a muzzle, as any type of crutch, on a fearful dog. I also have a shepherd that is wary of people. He's quite the opposite though. No chasing after humans and doesn't lash out when they're retreating in any manner. His issue is a straight on frontal approach with direct eye contact or intent to pet.
We've made a lot of progress with a "handshake" command. I had never thought about this type of command (nor heard of it) but with the help of a forum member, we hammered out some details and rewardable actions.
In a controlled atmosphere, he's now 9 for 9. 9 folks with fingers intact after standing directly in front of him and shaking my hand. He sits, wary as all get out and eye contact is still an issue, but he's fairly solid with just the outstretched hands connecting.
With the muzzle though, and don't get me wrong, he does wear one when I know I may not be able to control all aspects of an interaction/his environment (vet, moving thru a crowd, proofing desensitization training) but he's a different dog with it on. Much more clingy. I, on the other hand, have a much higher sense of security. With it off, I'm the different person, much more wary, whereas he has a much truer sense of himself and is more confident to react or not, based on the situation.
Balancing the dance between the trust in our training sessions and the real life scenarios is as much a learning process for me, about what's making him tick as it is for him, in learning what I expect from him. Some may feel that the process is long, as Mara and Connie pointed out, at least 18 months, but the bonding process you go through could not be more rewarding.
You're as much in tune with their reactions and they are with yours. Well, let me rephrase that, I'm sure these sharper guys will always be much more in tune with us but you're going thru the process together. You taught, you learnt, they learnt, you know, they know, trust is built - behaviors get modified (yours and theirs).
In your situation Suzanne, I would always have her on a leash around people right now. Perhaps there's some kind of "leaving" or "going away" command that you could work on.
Maybe the minute someone turns to walk away you could bring out a tug/ball or food reward. Have her "look" or focus on you as they step away and reward for her attention to you, not the leaving person. Teach her that people leaving sparks a fun time with you, nothing to be scared or nervous about.
10 months is very young but a lot can transpire thru those first impactful 10 months that can imprint some pretty fearful behavior. It's the age I rescued my shepherd. I was able to get a lot under control in the first six months with some basic obedience and life exposures but he was mess with just simple daily living. His distrust in humans was something that was imprinted at a very young age. I've had him for three years now and he's very easily managed, but managed he is.
I don't know if he will ever fully trust another human, to the point where he's truly willing to let down his guard and accept or provide some form of affection to/from them.
And that's okay, I only ask that he tolerates their presence, no one "needs" to touch or talk to him. And bottom line, he adores me. As a family member and companion, I could not ask for a more obedient, thoughtful or single mindedly compassionate dog. His bond is incredibly strong and couldn't be truer, almost tangible.
All dogs, regardless of temperament, require a fair amount of attention/training and need to learn what's expected of them.
No offence Suzanne but daycare, dog walkers, running amok on daughter's farm, bite, bite and now you're thinking nighty, night.
You brought a cute 3 month old shepherd home on a whim (when it sounds like you really wanted something smaller) and now she's growing up. It sounds like she's been handled more by everyone else but you at this point and they haven't been doing a very good job at instilling any kind security or rules that she can learn and live by. No sense of routine that she can take comfort in or any sense of stability in where she is going next.
What might be going on? I think you might be in a better place to answer that than many of us but personally I don't think it's anything that a stable home, confident leader, and some routine training that a dedicated dog owner couldnt take of.
I also agree with Betty. If you dedicate some time and training to her, I think you will have an incredible companion for your walks in New York City or anywhere you choose to take her.
I hope this all works out for you, she sounds like a great pup, simply learning and adapting the only way she knows how. A little guidance for this baby would go a long way.