Her behaviour is 'normal' and I suggest you avoid lying on the floor unless you want to be marauded by her
Simply sit on the floor with her so that you are in an upright position and you are then better placed to control her behaviour. Place a light lead on her so that you have an extra degree of control also. Puppies of this age always need to be mouthing chewing, so keep a rag type toy to hand so that can go into her jaw rather than your hands or nose. Any teeth on skin should be met with a 'No biting' in a firm voice and see if she settles down after your clear instruction.
If she goes nuts when you go to play with her and she seems uncontrollable, you can send a more clear message by placing her into a time out for a minute. Simply take her by the lead and drop it over something fixed such as a radiator or similar. It needs to be safe and secure of course. After the minute is up and she is looking calm let her off and try again. Repeat as needed.
Avoid shouting or heavy handling of course.
HTH,
Nick