A dog followed me home?

[Sidney]

I live out in the country, and there aren't that many houses around. Anyways, my cousin and I were riding down the road on our horses, and about halfway to the trail we were heading to we looked back to check for cars and saw a small dog following us. We didn't think much about it, and figured if it lived nearby it would eventually go home. Yeah, it didn't. It followed us the rest of the way to the trail(which is a quarter mile away from our houses), down the trail a little ways, and all the way back to our house. There are only about 5 or so houses in between the trail and our houses, and the people at the house closest to us said it wasn't theirs. On the way back home, the dog didn't even really look at any of the houses, and neither me or my cousin have ever seen the dog at any of the houses. We have only seen the dog a few times, the first time being about two or three weeks ago. The dog(a girl) is really skittish, but very sweet once she gets to know you. Anyways, I didn't want to leave a potentially stray dog loose running around especially since we might have an ice storm tonight, so I lured her close with a treat and put a leash on her and put her in a small dog pen with some food and water and a dog house. She has a leather collar on, but I didn't find any info on it, and it looks kind of old and dried out. We also put a picture of her and our info on Facebook to see if anyone recognizes her, but no one has answered so far. If no one claims her then I plan on keeping her. What should I do with her for now incase someone claims her? My parents want to turn her loose and see if she goes back home, but I dont want her to run off if she doesn't belong to anyone, you know? What should I do? Will putting her picture on Facebook work?
Also, what should I do if no one on Facebook recognizes her, but she still belongs to someone? I dont want to steal someone elses dog on accident...
Also, what should I do if no one on Facebook recognizes her, but she still belongs to someone? I dont want to steal someone elses dog on accident...
Also, what should I do if no one on Facebook recognizes her, but she still belongs to someone? I dont want to steal someone elses dog on accident...
Also, I forgot to add, the times we have seen her she was running around in our grandparents' large cattle fields or at my cousin's house sniffing around. (Our three houses are close together, but except for the one that we already checked, the others are all a pretty good distance away.)
just to make it clear, I do have three other dogs. If you would also look at my other questions, you would know I am working with them on ALL of that. I am taking them for long walks DAILY. I have been border training in the yard with them for the past 3 weeks using dog training flags, and I worked with them so that they ignore all the other animals. The way that I set up the borders, they cant get anywhere near the driveway/road. Also, I am putting up pictures of her on Facebook, Instagram, etc. DAILY.