Physical pain is possible through empathy. Only you can know if it was your cat's pain or your own. Usually the way to tell is to either acknowledge it is your cat (therefore not you) which can allow you to let go of the feeling. Or the easiest way is by walking far enough away and focusing on someone else. If the pain suddenly stops and then returns when you are in close proximity or begin to focus on the individual again, then you can ascertain that it is clairsentience.
From my own experience, pain doesn't always effect an empathic as it does the actual one hurting. Sometimes it effects the opposite side of the body or can register in a different place altogether (commonly in the form of stomach ache, headache, or back pain). This varies from person to person.
Empathy/Clairsentience is very personal. The way we interpret emotion and physical pain is different from person to person. Since empathy is picking up other's emotions/pain, we interpret it the way we would, not the way they do.
An interesting scientific fact. They have discovered that physical and emotional pain registers in the same place in the brain. Our minds cannot distinguish between the two. Therefore when someone is grief stricken or heart broken, their body responds as if they are in physical pain.