Hi there - I'm Dr. Sara. I'm a licensed veterinarian who works exclusively with dogs and cats. Bless you for taking on Miss Brynley as a rescue pup - I'm sure she'll make a great addition to your family :) I'm sorry that she's had some trouble adjusting, but we may yet see her come out of her shell a bit.
Dogs have a critical socialization window of time during which they are open to new experiences. This window closes at around three months of age, so whatever they'd not been exposed to in a positive way before that time will automatically be met with skepticism and even fear. Also, if they had a bad experience with something during that early time in their life, it can leave a lasting negative impression. It's for this reason that puppies who aren't socialized well during those early weeks of life can be much more difficult to socialize later. It's certainly possible to mitigate her anxieties, but it's going to take more time and work, and possibly the help of some medications.
The most important thing with a fearful dog is to try to countercondition them - that is to use high value rewards like food to try to distract them from their fears and also tell them that they don't have to be scared. It's a bit like saying, "Hey, I know that you don't like the rain, but when it rains I'm going to feed you something really great" This way, the next time it rains, she may start to look for food instead of go hide. There is a level of anxiety at which this won't work - if they get too scared, they just won't eat the treat. In those cases, if we can lessen the stimulus so that it's less scary for her, we can try again. With introducing people, I usually suggest giving the person some of her favorite treats and telling the person to basically ignore her until she comes around. When she does, your guest can drop cookies on the floor at first and potentially if she warms up can feed her out of their hands. Every dog is going to "warm up" at a different pace. Unfortunately, no matter what we do, some dogs have such severe anxiety that these tactics won't be helpful. These are the ones I consider a candidate for anti-anxiety medication. Anti-anxiety medication can lessen their anxiety enough that you can make progress with counterconditioning and desensitizing her to things that make her anxious. This would be a strategy I'd only consider after she's had a complete physical and with the guidance of your family vet.
Pheromone and herbal calming products like the Sentry Good Behavior collar and VetriScience's Composure Pro can also be helpful for easing general anxiety, however I find that they aren't enough to touch severe anxieties.
The most important thing here is to give her time, nurturing, and TLC. She's still quite new to you and your home, so with patience and gentle handling, she may come around without a whole lot of other intervention.
Please let me know what other questions I can answer for you - we can chat until we've discussed them all :)