I would suggest not paying her any kind of reassuring attention when she growls or cries because this is just rewarding her current behaviour.

Rather than stroke the other dog yourself and such, which doesn't work, it's better to just let her get to know the other dog on her own and you not interfere in anyway with the interaction. Maybe keep her on lead first so that you have control over her but if things get nasty, no shouting or saying anything to her for it and just very gently pull her out of reach of the other dog.

When you walk her, take some of her daily food ration with you, split into even smaller portions and, everytime you pass another dog, no matter how she reacts, feed her the portion of food. Once she is looking at you for the food rather than fretting over the other dog, you can graduate to just giving her a tit bit, playing with her using a favourite toy or just give her a nice fuss and a pat with some nice words. She'll learn that the presence of other dogs is a prelude to nice experiences and will start to look forward to seeing them rather than dread them.

Make sure she is wearing a type of collar or harness that doesn't cause her pain if she ever lunges out at other dogs and never punish her for growling or acting in these ways towards other dogs otherwise she'll blame the other dog for the bad experience and this just reinforces her fear of them.

When you introduce her to some dogs for the first time, pick a dog thats about the same size as her at first maybe and one that is calmer in temperament but gets on well with other dogs. If she ignores the other dogs, that doesn't really matter so don't worry about that.

Most of all, don't make a big deal out of it. When people overreact to these situations, thats what compounds the problem and makes it worse. It's important for you to remain calm and relaxed as possible when other dogs are around because any tension you feel will transfer to her.

When she was with the puppy you mention, did she stop at just growling at the pup? If so, do not worry. Many dogs do this anyway just to assert their dominance over the pup and this behaviour would calm down after a day or two if the two dogs were together a lot of the time. Our Mist used to do this to new pup arrivals in our family but never hurt one and would settle down pretty quick and actually become quite protective and motherly over them.
She'd seem really mean at first and it was all too tempting to tell her off for being nasty but that would have caused "Real", problems. These things have to be sorted out by the dogs on their own. People interfering is what messes everything up. The pups knew what Mist was telling them and thats all that counted. It was normal for them, their language, certainly not cruel.

Good luck in making her more dog friendly.