Just stopping by again to give an update on my game:
I repaired through Origin and that fixed the issue with not being paid. My Sims get paid automatically after treating a pet like they should now, but I'm still having problems with pets getting on and off the exam table several times in the middle of the exam. It makes examining and treating one pet take half the day. :neutral:
I know lots of people are saying having your household pets on the vet clinic lot is what breaks the vet clinic, but since repairing, I have had no issues with payment and my Sims live at the vet clinic with their two cats and one dog so the pets are always there. The whole family is.
To clarify in case that confuses anyone; my Sim does own a separate residential lot. He has to because you can't officially "live" at a vet clinic, but his home lot is just an empty lot that he never goes to. I built an apartment on the second floor of the vet clinic and that is where my Sim lives with his family. They just stay at the vet clinic 24/7 and treat it like their house.