There are ways for someone who is allergic to cats to have a cat. Ask your vet.
The other thing I was thinking, your post got buried in this - might it be better to cut and paste it to its own post? Maybe more people will see it if you title it something like loving cat needs a new home?
In the mean time I would build a cat shelter in your backyard. I’m worried that with winter coming your beloved kitty might not make it.
I have been warned by more than one person to be careful when “giving a cat/kittens away for free”. Apparently some very despicable people out there will take advantage and use the cats/kittens as live bait for pit bull fights or snake food.