Picked up a friendly stray -- No one will adopt her. What should I do??

Hey everyone! I'm new here, but I really need some help/support right now. My story is a bit lengthy, but please bare with me. 

About a week ago, I noticed a small-ish cat roaming around the parking lot of my office. There are many cats that hangout around there, but this one kept turning up, and meowing at me from across the parking lot. So, I started leaving for out for it, and working with it to get it accustomed to being around humans. My original plan was to get her (she has a "Tortoise Shell" coat, so I am just assuming it's a girl) more comfortable with me, so I could take her to a local TNR (Trap, Neuter, Release) clinic, without freaking her out so badly. Within only two days, however, she quickly grew comfortable with me, so much so that she would come to me when I made a certain noise, and she let me pick her up and love on her. This wasn't something I expected, but was a happy surprise. My plan remained the same, however, until I noticed that she was using a car engine as a place to sleep. At that point, I just couldn't leave her there another night, especially considering that she was so sweet, young (probably no more than 5 months), and so very adoptable. My new plan was to take her home for the night, and wake up the next morning and take her to my local NO-KILL shelter, because I knew that she would be able to find a home quickly there. However, when I took her to the shelter the next morning, they all but kicked me out the door because they claimed they didn't have enough room for a cat that wasn't basically a newborn kitten. This was a let down, but I didn't let it deter me, yet. I spent two days calling vets, no-kill shelters, foster home organizations, and posting her story to every local facebook page, lost and found ads, etc.. And, even though I did all of this, absolutely nothing has come out of it.  All the no-kill shelters are full. No one on facebook seems to want to do anything but "pray" for her to find a good home, and I am having a hard time not getting discouraged. 

You see, I would keep her in a heart-beat, if I could. However, I am going to college in the Spring, and simply cannot take her to live in a dorm with me. My family has two dogs, that she does not like in the slightest (I imagine that's because she was a stray, and views anything that's bigger than her as a predator). I feel like I have exhausted every effort, but I still cannot find this little girl a home. I'm not sure where to go from here. I could really use some help, and suggestions. 

Also, I guess I kinda wanted to know if anyone else is having, or has had a similar problem as me? I can't help but feeling extremely alone in caring about her well-being, considering that everyone keeps turning her away, and no one seems to want to take her in. 

I feel so sick when I think about possibly having to simply spay her, and take her back to my office parking lot. I don't know how to fix this situation. I was just trying to help her. 

We've all had this experience.  I was very fortunate in that my no-kill shelter was very helpful.

You might try posting her picture at work, too, and perhaps in the surrounding neighborhood.  Anything to get the word out will help.

After you spay her, is there a possibility she can stay in your parents yard/garage/your old room?  If you take responsibility for her (paying for her litter and food), would they be willing to keep her until you are on your own?

If you attend a church, post a notice there, too.  Good luck and blessings on your for stepping up to the plate here.

You're living with your parents until next Spring, right? Is there a way you can keep her in your room? It wouldn't be an ideal situation but it would be so much better than her living in a parking lot or shelter. You'd have several months to either find her a home, or it's also very possible that she and the dogs would adjust to each other over that long amount of time. Cats and dogs do very often learn to live peacefully together. As in any situation where a new cat is brought into a household with other cats or dogs, there is always a time of adjustment between them. I hope you will consider taking the kitten into your room while you continue to find a home for her, or until she would adjust to your parents home and even find that home to be a very loving place. Thank you for taking care of the kitty.