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Hello I am Dr. Pulter. I am reviewing your question and will reply ASAP.
There are many things that could be wrong with your puppy. Here is a list of possible diagnoses based on your question - intestinal blockage, congenital malformation, parasites, infection, pain or something else. Tonight make sure your puppy is properly burped and stimulated to pee and poop if the mother does not do it. The puppy will need to be seen tonight or tomorrow as the most concerning possibility is an intestinal blockage which could cause life threatening illness. As a disclaimer the information provided is general and does not take the place of a physical exam, consultation and diagnosis done by your veterinarian on your pet.
I definitely agree that you should worm at 2 weeks. Have you looked inside this puppy's mouth? Sometimes a cleft lip can cause milk to run into the nose to cause irritation and congestion, especially if this has been happening since birth.
I am sorry that this one is sick. He definitely needs more care and attention. Do you have a bulb syringe? You can try suctioning out some of the mucus and can also have him in a bathroom with some steam from a hot shower to help break up the mucus. You can check to see if he has a fever with a rectal thermometer (normal is 99-101).
I would just suction the nose. I think if the temperature is normal it does not rule out infection or other issues with this puppy. Runt's tend to have lower immune systems and generally don't do as well as their counter parts. This puppy may need an exam sooner than his 2 week mark.