This is one of the reasons for NOT getting a puppy so young. When they are taken away from mom and siblings too young, they lack that sense of security that helps them rest and go to sleep on their own. As "crazy" as you and your DH are, think how the puppy is feeling. They do not like to whine, or stay up all night. If you are sleep deprived and exhausted, the puppy probably is too. Another month and the puppy will be much better adapted to sleep on its own and hold it's potty breaks at night. That is why I would not let mine go to new homes til they were at least 12 weeks old and older if they needed it.
Try to buy one of those heartbeat/warmer dogs -- it is a stuffed puppy that has a pocket in its belly. You put these warmers in there along with a little heart that gives off a "beat" -- they are great for reassuring those tiny puppies taken away from their mothers too young. I bought them for my puppies when I lost a mother dog. If you cannot find one, you can use a rice bag, wrapped well with a towel along with a wind up alarm clock. Other than that, the only thing that will help is time.
The problem with biting your fingers too hard can be seen more in puppies taken too young too. Truly, they learn some reserve while being with their mother and siblings. They learn that when their siblings bite, it can hurt. They learn if they bite their momma, she will gently nip them to teach them not to do it. So, you have to become the momma and sibling. Gently nip (with your fingers instead of teeth
) the back of puppies neck and say firmly "no" or "ow." Eventually, they learn that is not a good behavior. It takes longer, because I was never willing to really hurt them. Instead, they just learned it was a tone of voice that they did not like as much as the "good boy" tones. So, it takes longer than the momma nipping them into better behavior.
Hope these things help.