Hi, My name is Philip. I am an attorney with over 16 years experience. Hopefully I can help you with your legal question.
I am very sorry for your dilemma.
The answer to your question "Do I have to pay for their cart damage?" will depend on who is at fault for the damage.
This area of the law is called "tort
liability". Under tort law, if one person caused harm to another, they are liable for the damages the cause. For example, if a person,lets call them A, is driving
their car and, through their own negligence, they run into another car, lets call them B, then A would be liable for the damages to B and to B's car
On the other hand, say in the example above, say that B is driving a car with no tail lights. And say that A is following B. B applies the brakes, A runs into B. IN that case, most likely B will be liable for damages to A's car since B did not have proper lights installed.
In your case, the way you describe it? It sure sounds like you were negligent...that you were responsible for the accident. If so? You are liable for the damages. This is true despite your injuries.
On the other hand, if the cart was defective...and that defect caused the accident? Then not only would you not be liable for the damages to the wall and the cart but they would be liable to you for the cost of your bills.
SO really this is a matter of who is responsible.
If you can point to some problem with the cart that led to this? It may be you can negotiate with them to limit what you pay, or even demand they pay you.
Otherwise, you will be liable for the damages caused in the accident
Let me know if you have more questions...happy to help if I can