How do I keep my dog from using my hands and arms as chewtoys?

My sister and I have an approximately 6 month old labrador/beagle mix. She has been with us for about 3 months now, and we're still having a really hard time with her. She has this really intense energy that nothing seems to quell. We take her on long walks, play catch with her, give her toys, etc. But she never seems to calm down. We've even tried herbal calming treats... When she is inside and out of her kennel, she just runs around the house in circles, jumping around like she's insane... I've never seen a dog that could jump as far and as high as she can. She tries to chew up everything in her path, which I know is normal, but of the things she enjoys chewing, it seems that our hands are her favorite. I keep trying to do research on dog biting, but hers is so different from what I find information on. She doesn't do it with malice...it's very playful. She bites and then she just starts chewing on my hand...And she can bite hard! I have a hard time getting my hand away from her. I have tried every tip that I could find online about training a dog not to bite, but nothing seems to take effect. She doesn't respond to me saying "NO!" no matter how stern my voice is, she doesn't care if I pull on her collar, saying "owww" in a high-pitched voice doesn't matter... I have also tried holding her mouth shut for a few seconds and ignoring her. When I ignore her, she probably bites even more to get attention. I usually have to end up putting her in the cage to avoid being seriously hurt. She has never growled at me or acted aggressive toward me; it's not that. She chews on my hand like it's no big deal and looks at me just like she would when she isn't, and her tail just keeps wagging. Obedience training is out of the question right now...I just can't pay for it. I want to be able to let her spend more time out of the cage...but now the only time she behaves herself is when she's outside. Any suggestions? (Especially for the biting!)