Stray dog in need of help!

Hello, recently a stray dog followed me home from when I pet it at a bus stop. He was very friendly and I assumed he was a neighbors dog, who was unnaturally thin. However, recently, I've come to realize he is a stray and probably dumped.

However, I can't take care of a dog. He won't lave my front yard, begging for me to take care of him. I called BARC yesterday but they didn't come for some reason. I have no idea what to do. I'm a college student with a cat already. It breaks my heart but I genuinely can't care for him or help him, as he has an I jury on the side of his head.

So if anyone can help me or give me guidance, please. I don't know his history but he seems like a very quiet and loyal dog. I've never heard him Bark and he seems so happy even though he either got out or was abandoned. He acts trained and keeps trying to walk into my house. My only other options are leaving him at the barc shelter, or the rescues I've reached out to. However, I genuinely can't afford him. And I don't know what to do if they turn him away.