Hello, my name is***** and I have over 20 years of experience as a veterinarian.
I'm sorry to hear that your pup may swallowed a big chunk of a pizzle stick.
The good news is that these are digestible, although they do take more time and digestive juices than most things.
How concerned you need to be depends upon your puppy's size and his level of comfort.
If your puppy is a large breed dog if things seem to be well at this point I am less concerned. But if the chunk was big and if your little one is still very small then I would be a little worried.
If your pup appears to be fine then in this case we need to try and hope that we can get the stick to pass through the gastrointestinal tract. And that his stomach acid helps us by dissolving the fragments.
For the next few days, until the pieces pass, you may want to feed a soft, bland diet with lots of fiber added in small meals several times a day, 4 to 6 meals is ideal. We do this so the pieces are surrounded and don't get stuck, the gut isn't irritated and isn't contracting on just sharp chunks.
A homemade diet for this is 1/3 boiled, lean hamburger or boiled, white, skinless chicken, all fats drained off the meat, and 2/3 white rice. Add 1-2 tablespoons of canned pumpkin, (not pie filling, just pumpkin), depending upon his weight (bigger pup, more pumpkin), to each meal for fiber.
Signs that things aren't going well, and he needs an immediate veterinary visit, are vomiting, a tense painful belly, lack of an appetite, a fever (more than 103.5F rectally) and lethargy.
If it doubt at all that things aren't going well it is always best to have him checked.
After 3 to 4 days if he's still feeling well and passing normal stools then start mixing in his regular puppy food, adding a little more regular and less bland at each meal. It should take 5-7 days to get him converted back to regular food.
Let me know if you have any further questions.