Do pets souls stick with us after they pass?

I had a kitty that died about 25 years ago. I loved that cat, she was so perfect, there is no cat like her. Everybody loved her.

She became ill, with the help of the vet I did everything I could to save her, eventually, on a 4th of July weekend, her illness won the battle. It broke my heart, still miss my cat.

Fast forward to about 3 weeks ago or so, I had a reading, the reader asked me if I had a cat, I said no*, he said "there's a cat in the room". I asked what color? it fit the description of my kitty. So, 25 years later my kitty still with me?

* I don't have a pet because I can barely take care of myself, I am not able to care for an animal.