Is it normal to feel guilty about getting a second pet

When something new happens, a big change I get depressed.
When we got our cat we already had one and I didnt even know we were getting a kitten he was just there when I got home and at first I felt very depressed about it because I was already so attached to the cat we had and couldn't even imagine loving another but very soon I did and now he is best baby and he literally owns my heart forever and always.
Now i'm getting a new pet tomorrow. I was extremely happy and excited but then my lovely cat came and started following me around even more affectionate than usual like he knew what's going to come and I started to feel bad and got depressed and felt bad that I could even imagine loving another pet. I guess that's rather strange, many people own several different pets just like people have more than one child. I wonder if those people ever felt bad at first or i'm too sensitive.