I am going to start off with this, I am a vet tech (a highly educated one, not just the person who holds the dog at the vet, more like a nurse practitioner for pets) You would have to have the worse vet in the world to have messed up a neuter that bad where something was not put back together properly. If it were a female I would say the vet could have tied off the ureters by mistake while spaying but that is really rare.
What you need to do is have a urinalysis done to rule out infection or crystals (which bind together and from stones) in the urinary tract. In all honesty if it where my dog I would have an x-ray done to make sure there was not a bladder stone (very common in dogs).
I hope everything works out but I would go to another vet and have these test done.
If you can’t afford to go right now go to GNC and buy some cranberry supplement and give it to your dog it won’t hurt anything and may help if there is an infection or just crystal formation.
For legality sake I am not a veterinarian and this is just friendly advice given to an online buddy.