What others have said - prong collar is kinder and more effective than a choke. A five month old working line of high energy and drive needs more exercise than leash walks. I know that winter is a challenge (check out my location), but if you can find some open place out of the way where you can REALLY work her and tire her out, it's worth the effort.
You may need to work with a trainer one-on-one that will gradually introduce distractions in obedience training, and can help you get control. You may be inadvertently triggering these behaviours in your pup with your energy and body language and movements when in class - saying this because your pup worked well for the trainer. The trainer should be helping you find that balance with your dog.
Are you tiring out your dog before class? Long walks, running, playing fetch? Many people need to really exercise their dogs before training to help them settle and focus.
If your dog is as high energy and as high prey drive as the trainer said, play ball outside in the snow - running through deep snow is a great way to tire out your dog. Also look into getting a flirt pole - a life saver for exercising pups when space is limited.