Cat had her vaccine appointment a few weeks ago but got a call last week from them telling me they did not give her one of them even though I paid for it. How do I tell them I will not be paying for anything today?

Just like the title says. This is particularly upsetting because my cat is extremely difficult to get into her carrier. I have had to cancel so many appointments because I couldn't do it. I also live an hour away so having to go back is a major inconvenience. They told me on the phone they would not be charging for the vaccine, but I am concerned that they will charge me for an exam fee and other things. I refuse to pay for anything since it was their error but have no idea how to approach that. I am fairly nervous about situations like this so I would love some advice.