"front legs" meant to say ;o)
No thats not normal. Just incase you don't this, you probably do, but when picking up a puppy, you must put your hand over his tail - supporting his rear as you lift - with the other hand under his front arms. Most times its easier to do from behind the dog or his side.
I've seen people lift dogs and puppies by taking their hands and putting them under the dogs armpits and lift. The weight of the lower half of the body will be a strain on the dogs back and they can get hurt. You probably know the correct way to pick up your dog, but just incase I felt I should mention it.
If that was not the reason for the yelp, I would definitely call the doctor and let him know that she seems like she has pain.
Good luck with your puppy.