Yes, it's entirely possible for a cat to have FIV. I, personally, don't know much about it, but there are many here who do and hopefully they will give you much more insight than I can. One suggestion would be to do a search, here on Pet Talk (far upper right corner) and type in FIV. If you don't find anything, do a google on FIV and I'm sure you'll find more information than you could ever imagine.

Good luck and I sure hope your kitty is healthy for a long time yet! Oh, and welcome to Pet Talk!