Best way to give a kitten up for adoption?

I rescued a kitten off the streets a few days ago. I believe she is about 6 weeks old and I think she lost her mother because when I caught her she was nothing but skin and bones. We have fallen in love with the little thing and my brother and I have been trying to convince our parents into letting us keep her. My mom really wants to keep her but says we can't and my dad likes her but says pets are too big of a hassle. The cat I currently have was rescued off the street and I was able to get my parents to let me keep her but I don't want to make them mad and feel disappointed with me. So I'm trying to find a way to give her up for adoption if my parents don't change their mind.

I have already posted it on my Facebook and even asked relatives. I'm in college and I was apart of a group and posted it there and no one will take her still. I will not post it on Craigslist because I know how easy it is for evil people to be on there searching for animals to abuse and I couldn't live with myself if she goes to someone who is evil. One shelter I contacted already doesn't have room but said they could try to make room but if she acted feral at all they would put her down. The other shelter won't take her because I found her in city limits and even if they did their rules are still the same as the other. There is one no kill shelter in the next town but they are full! They already have almost 100 cats.

Another issue is that she doesn't have any shots and hasn't even had a check up and I know a lot of people want a kitten who has had all of that done. I have a job and pay for my cat already and I just now was able to build my savings back up. (During winter break I had to buy books and take care of my rat's medical bills and together those things cost quite a bit over $1000). The fall is going to be here before I know it and I will have to dish out over $500 on books (I do amazon and buy used books whenever possible). I want to and plan on taking the kitten to the vet soon but I'm so afraid that she might have heart worms or internal parasites and I know that will be expensive to treat and it will be hard to find her a home if she does and it will be hard to pay for. And I know you never post online a free kitten and to do an adoption fee and I would base that off of medical cost (not the whole cost but at least part of it).

I know there is petfinder.com but I have no idea how to post on there. If someone knows and could tell me I would appreciate it. But I was wondering if there were any other good sites out there where I can post her and have control over the adoption? And if she does have heart worms there is no cure for it in cats and she would have to go to an extra special home who will be able to take her to the vet more often. Is there a site or an organization for pets with special needs that need to be adopted? Or is there a way to find foster homes in the area where I can keep in contact with them like, if she is adopted I can be notified so I don't worry? I don't think you can do that with shelters. The only way I would drop her off at a kill shelter is if they would make a deal with me that she is to be put down I would adopt her back but I don't think that is possible. One other reason why I'm against shelters is that I know she probably won't have a hard time being adopted but if she is chosen then that could mean another cat (even one that is maybe only a year old) could be put to sleep because they chose her over the other one. That would make me feel like a horrible person if that happened!

Of course more than anything I want my parents to change their minds. I have been responsible with every single pet we have owned (I spent around $650 in vet bills on a 3 year old rat who started having issues)! I have a huge heart for animals and I want them to all have a great life! Which is the main reason I couldn't leave her along a busy street to die!

If someone could help me I would greatly appreciate it!