What should I do with this stray dog?

A stray dog showed up outside my apartment a few weeks ago. Idiotically, I fed it because it looked hungry, and it obviously stuck around. A few days later it was snowing and the dog was barking outside my door, so I let it in. I put it outside 2 days later once it was warmed up a bit, but it keeps coming back! It’s barking gets really annoying so I let it inside (since it’s a rather small dog).

I put an add in the paper, called veterinarians, and put up various signs, but I’ve gotten nothing. I’ve called the only 2 non-kill shelters in the area and they both say they’re full!

I absolutely cannot keep this dog, and none of my friends want it. Also, the only other shelter puts them down after 2 weeks.

What should I do?