Yes, perfectly normal for a puppy to be mouthy. One, it's their way of exploring the world and two it helps with the new adult teeth coming through, like a human baby.
But I would definitely redirect from her chewing at you to chewing a toy, it can get painful believe me. You can get puppy chew rings, which are kinda like baby teething rings only stronger, or just buy her some good chew type toys. Kong have toys for all sizes and ages, a bit more expensive than some toys, but they LAST!!!!!!!!!
A little gentle mouthing is fine, just use a cue like 'gently' but it can get to be very hard as she grows a little more, so let her chew gently but also introduce her chew toy, that way, as she gets older and there's a chance the mouthing can get harder, it won't be a huge problem.
Some puppies, like my late gal Tiger Lily are always gentle, but her Bro Zeus (my golden oldie) was the opposite.
Ra Kismet my youngster was very mouthy and painful with it too right from the start
. So it does differ with puppies, but it's all perfectly natural
You're lucky, seems like you've got one of the gentle ones.