My Maltipoo does the same thing...I call it 'corn cobbing', and it's a carry-over from puppy hood.
Mouthing/biting is a very common behaviour , who have very sharp baby teeth that are falling out to make room teeth. Depending on the breed, this teething period and the desperate need to chew to soothe sore gums can last up to a year. I'm not sure what type of dog your puppy is, but a lot of herding dogs, such as border collies, tend to use their mouths when they're playing. They have been bred to herd cattle and sheep by nipping at their heels. Some hunting dogs, like labs, are also particularly mouthy.
Whatever the breed, the nipping and mouthing is still painful. Bitter Apple spray (which you can find at most all pet stores) is usually effective because most dogs can't stand the taste. But there are always exceptions to that rule. An effective alternative is breath freshener spray. The minty taste is far from being a canine favourite. You might also try dabbing your hands and arms with pickle juice. The juice contains a very sour additive called alum, which keeps the pickles crisp but is also a great dog deterrent, if you can stand the smell yourself!
It is more important, however, to train your pup not to nip, than to rely on repellents. She is bonding with you and needs to know that her nipping hurts. Around eight to ten weeks of age, puppies in litters learn about bite inhibition. When one puppy bites too hard and his sibling yelps, he learns to soften his play bite. So when your pup mouths you too roughly, you need to yelp loudly. In addition, you need to stand up, turn your back on her, and walk slowly away. The message is, "You are not fun right now, and playtime is over.". Your pup wants to play with you and when you walk away, she will learn that mouthing ends good times.
That said, your pup is likely at an age where she NEEDS to chew. When she gets in a mouthy mood, offer her some suitable chew toys as a substitute hands and arms. When you play with her, use thick rope toys or rubber tugs that provide something safe to put her mouth around while protecting your hands and arms. Please resist smacking her muzzle or holding her mouth closed as these punitive tactics can backfire and cause her to bite more, and harder.
I hope this helps!!