well it sounds like she is very bonded to you, and looks to you for confidence / reassurance. She could also be resource guarding you, (the snapping at other dogs) but believe me, a dog that young is not protecting you.
I agree with Diane - either resource guarding you from other dogs, or she's more confident with you there backing her up.
We did some interesting training with Cassidy, who was VERY leash reactive around other dogs. She was fine with most dogs off leash, and we used to go to the off leash park to play ball and let her swim all the time. It was called Abandonment Training - we held her leash while a trainer had a long line. An assistant walked another dog into view, and the second Cassidy saw the dog at a distance and started to tense, but before she blew up into a reaction, we tossed her leash at her (the tactile sense of the leash hitting can break through and get the dog's attention when their other senses, such as sight and hearing, are otherwise engaged), and turned around and ran in the opposite direction.
She'd realize we were gone and she was all alone to challenge this dog by herself. After a brief "oh, crap!" moment, she'd turn and run to us for a big reward. She was still under control because of the long line, but she felt like she was free, and consequently she had the choice to leave, like we did, rather than stay and engage. Her natural inclination was more "flight" than "fight", but the leash can inhibit normal greeting behaviors by dogs and take those choices away from them, causing fear, stress, and social anxiety - hence the aggressive display, which is designed to scare away the other dog.
Within about 20 minutes she and the other dog were walking calmly past each other, about 3 feet apart, with no reaction.