Always been a cat lover, and intended to have one when I move out and get a place for myself. That said, I found a stray cat outside my house today coming home from my internship. Thought it was cute, and whatnot. Even played with it for a little bit. I found that this cat has absolutely no body fat, sounds like it has trouble breathing (I can hear it breathe, so I'm assuming there's a problem; I"m not sure if cats usually make a sound when they're normally breathing), and won't leave my porch. Played with it around 7pm, then went to eat dinner and whatnot. My family gave it some milk, and it lapped it up eagerly. Afterwards, we tried to shoo it away, but it wouldn't budge. We yelled, made threatening gestures at it and whatnot, and it wouldn't budge.
I just went to check on it like ten minutes ago, and to my horror it was sitting down in front of the door, and when I opened the door, it tried to come inside my house. I had no choice but to close the door and deny it its entrance (stray cat; don't know what kinds of diseases it has, etc., and my mom and brother are slightly allergic to cats). I'm sure if I go check again it'll try to do the same thing.
My estimate is that this cat will most likely die within the week even with us giving it milk (it was so starved). I can't keep this cat for reasons stated above, and it won't move away. What to do?