"See" was also given as a translation for "nhin." Could this also be "I see my cat"?
On another issue, why is this not "cua minh"?
Nhìn = look
thấy = see
I would say "look at my cat" is the most accurate here. "I see my cat" would be "Tôi thấy con mèo của tôi."
"cua minh" = of oneself. It's not always clear who the owner is. It's good to know but you should try to be more specific and use của tôi, của bạn, etc.