If you used hartz piperazine, then it is not very effective. So I will not count those dewormings.
All vets use pyrantel pamoate, in puppies, for roundworms.
You can by "strongid-t," with the main ingredient "pyrantel pamoate." At the pet store or online.
So if he had round worms this week, it will take at least two more dewormings. The pyrantel pamoate must be given two weeks apart. So two weeks from his last deworming, he should be dewormed again.
You will not always see the worms come out the hind end. That only happens when they have high numbers of worms.
If his fecal test was positive, then he still has roundworms until he gets at least another dose of de-wormer. It may take a total of 3 doses.
He may be feeling bad from his vaccine. That is pretty common.
The mucous means there is inflammation in the large intestine. That could be from the de-wormer or the worms dying.
You can give him human pepto bismal. The dose is 1 teaspoon, per 10 pounds of weight, every 6 hours as needed.
See if he will eat some plain cooked chicken and white rice. This is a bland diet for dogs and easier to digest.
Keep rubbing syrup, on his gums, every 2-3 hours until he starts eating.
If he is not drinking well, give him pedialyte with a syringe, or eye dropper, until his gums feel nice and moist.
Heartworm prevention also prevents roundworms and hookworms. So the sooner you can get him started on that the better.
I hope this helps.