Believe me, I know how hard it is when you lose a pet who is actually your family. I hate calling them pets because they ARE family.
It sounds like the cat from next door knows that you need some Kitty love, but you're not ready to have another cat. It might happen someday, but in the meantime you can certainly enjoy the love that you get from this cat. 
I absolutely love animals. But I'm allergic! I grew up with dogs and cats and I never had any problems with allergies until I was in my forties.
Dogs don't bother me nearly as much, and I would love to have one, but can't afford to fence in my yard. I live in Coyote country and I would absolutely have to do that.
I am terribly allergic to cats. And it makes me so mad because I want one so badly.
So when my neighbors go on trips, I volunteer to take care of their cats and dogs. That way I still get the joy of being around them. But I can go home to a dander free house.
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