In the evenings, puppies often have a crazy half hour with zombies, mouthing etc. If you can, prevention is better than cure. They are like toddlers - tired but they don't know to settle.
So, maybe have something like a frozen Kong for that time, licking out the filling will be soothing and he may just fall asleep.
For the biting specifically, this is just an extension of the boisterous play he had with his littermates but he needs to learn this is not how to play with humans. Some people find a sharp 'ouch' works but it can just ramp up the excitement. Some people find putting a toy in the dog's mouth works, others find the puppy is still more interested in nipping hands. My preferred method is to teach him that teeth on skin equals end of fun. So as soon as he makes contact, walk out of the room for a few moments. As long as the whole family is consistent - do it immediately and do it every time - he will learn. You could use a house line to draw him away, which keeps your hands both out of reach and also keeps hands for only good things.
You could also work on some training.
Incidentally, a three month old shouldn't be having a lot of exercise as his joints and bones are still forming. 15 minutes, a couple of times a day, would be around the recommended time.