It sounds like the new cat is more for your cat than for you. Try to be calm and just see how it goes over the next couple of weeks. If your first cat doesn't take to the new cat, consider cat therapy or even returning the 2nd cat. I know how awful that sounds but I also know that way back when, the same thing didn't work out when I did it. My baby was bullied, starved, and miserable. After a few months I had to return the 2nd cat, much to my dismay, but my baby perked right up and lived a long and happy life.