Why are you going to neuter him so early? (Just curious...)
Sounds like he loves you a lot... when I walk in the door, I allow mine about 5 minutes to spazz out before I even ask them to chill... they are just so darned happy to see me!
Careful with him in the front seat... airbags kill small dogs. I use seatbelt harnesses that snap into the seatbelt buckle, in the backseat... 4 dogs loose in the car is a road hazard!
Relax... enjoy his puppyness, it will be gone all too soon, then you'll have years to enjoy him as an adult. Puppies are only puppies for about one year!