This is often broadly called 'leash reactivity', and a fairly common issue with many dogs. It's important to keep in mind that this is a very vague, broad umbrella term that people use for everything from serious, active, 'my dog wants to kill that other dog' aggression to 'my puppy doesn't know leash manners yet and gets super happy-excited when they see a person', but it can be a useful phrase when trying to research and learn more about the behavior.
My first suggestion is to check out Feisty Fido by Dr. Patricia McConnell - it's a great primer on why this behavior happens and how to work with it (and why the techniques work). Not a very long book at all, and quite affordable, as well as available immediately as an e-book. It's written in a very logical, easy to understand way and doesn't require a lot of dog experience or dog behavior knowledge. The muzzle idea is wonderful - the reality of her breed is that if anything happens, even if she's not at fault, she'll likely be blamed, so having a tool like a muzzle that sends a signal to other people that maybe they shouldn't let their rude dog get in her face and reduces the risk of her causing serious damage is a good call. Check out the Muzzle Up! Project
for great advice on choosing a muzzle and training a dog to wear it happily and comfortably.
My second suggestion is to consider a consultation with a dog trainer or behaviorist who specifically works with reactivity issues. Many are doing remote consults these days. I suggest this because this is your first dog, so it can be really valuable to have experienced eyes watching your dog and talking you through what's happening. I'd suggest looking for someone certified through a reputable third party, such as the APDT
. These organizations only certify trainers and behaviorists who have demonstrated a certain level of scientifically backed knowledge about dog behavior and learning, and/or who have put in a certain number of hours doing hands-on training (depending on the level of certification). This helps turn the odds in your favor that you'll find someone up to date and knowledgeable about modern dog training, compared to just picking someone at random, because 'dog trainer' isn't a protected title, so essentially anyone can call themselves that and take your money, even if they have no idea what they're doing. There's still the occasional bad apple that gets through a certification program, but it's a good place to start!
Overall, I agree with the rest of the advice you've gotten. Work on focus and bonding indoors whenever possible. She doesn't know you or the area well yet, so she may be feeling extra insecure and on-edge, which won't help matters. If she's whining about the other dogs when you're working at distance, you're too close. If possible (easier said than done, I know), move even farther away until she can look at the dogs without getting worked up at all. Your goal shouls 100% be 'will ignore or behave neutrally around other dogs', not 'will play happily with every dog ever', and with that in mind, try to avoid her ever meeting other dogs on-leash if possible. This might sound silly now, but even if she calms down and seems interested in other dogs, you do not want to teach her that every dog she meets on leash is a potential playmate or social hour, just part of the environment that doesn't concern her. Even with her behavior and the muzzle, you may find the occasional person who wants to approach her with their dog, so be prepared to be her advocate (and even rude if necessary) and tell them firmly that no, she needs space, your dog can not meet my dog.
This kind of behavior could be dog aggression (genuinely wanting to attack and hurt the other dogs because they're other dogs), but it can also be fear based (putting on a big show to get the other dog to go away, because the leash means she feels trapped and can't run) or even excitement/frustration (wanting to go say 'hi' SO BADLY that she throws a tantrum because the leash is preventing her from getting over to them). With her age and history living safely with other dogs at the foster, I'd suspect it's one of the latter two, not the first. But you absolutely should be working on this now, while she is still young and learning, so that you get it under control and it doesn't escalate as it becomes an ingrained habit. This behavior IS something that can be improved, especially with early intervention on a young dog!