Woke up this morning and there was a sick stray in my garage sleeping on a pillow. It has cold like symptoms (sneezing, cat cough?, runny eyes and nose) and it is really skinny. I fed it and it ate like it was starving. All it is doing is sleeping, but will get up to be petted. I think it was abandoned or a house cat. Should i try to nurse it back to health and give it a chance or take it an animal shelter? I called and they said if it is unrecoverable it will cost 25 to put it to sleep. Of course I dont have the medicine for it and the shelter might, but they also may just put it to sleep.