My name is no name!

I found this kitten in front of my home and have been fostering it after not being able to find an owner. My roommate is allergic therefore I cannot keep it. I love animals so I could not help but take it in temporarily but I am having issues finding it a home. My local animal shelters have suggested I stick the cat back outside and stop feeding it. I keep referring to the kitty as It because I am unsure if they are a boy or girl. The kitty is very friendly and playful. It like to climb up onto my lap. It sleeps through the night and is having healthy bowel movements and a clean coat. I estimate it is about 8 weeks old. It maybe weighs 3lbs. Kitten has been such a joy to have these past days but I am in no position to keep them. I am hoping to find it a home quickly and would be willing to help get it vaccinated.