I will say the description you provided is unusual. Difficulty pooping in puppies is most often caused by dried poop stuck in the hair around the anus, called a fecalith. It can also be caused by true consitpation.
Here is some info that may help:
I don't worry about a puppy not pooping unless the puppy is trying but unable or if there is an affect on attitude or appetite. If your puppy is eating well and feels good he will poop when needed. For safety check to make sure there is no dried poop in the hair around the anus as this can cause the puppy to delay defecation because it is uncomfortable. If there is dried poop in this area you can gently bathe it away with warm water and a little mild dish soap or if you have a small hair trimmer you can clip it out. Using scissors for this should be avoided as it is very easy to injure your puppy.