I got my first kitten last summer. I had an older cat growing up, and my husband had a few cats when we met but they were all older. I wanted a kitten and a friend had some so we ended up taking one in. She was all by herself, no other cat wanted to play with her. We made sure she had TONS of toys to play with, got lots of love etc. We would bring her into the bed when we went to bed (she was so small at first we wanted her locked with us) and I would hold her on my chest so she could feel my heartbeat, and lightly stroke her nose/head til she was sleepy, and she would curl up with us.
Kittens are so funny. I know you said you can't get another kitten or anything, but kittens in pairs are amazing. We had Katie last year and she got kinda mean and distant after awhile. I started working from home, so we adopted Joey back in April of this year. Joey just wanted to play ALLLLL the time, and Katie was still young, so he played with her a lot. We had to wear socks all the time because Joey's favorite game was to bite our toes when we walked.
A few weeks later, we had the chance to adopt a blind kitten that was going to be abandoned/put down, and he was about Joey's age. They bonded immediately...Now, 3 months after that, we found a kitten outside scrounging for food in our chicken coop. Toby was about 8 weeks old, and once he got over his sickness, he is now so bonded to our other kittens. They sleep in the same areas, play together all the time, and are adorable. We throw some balls with bells in them into the kitchen and they "play soccer" with them. We use dangly toys, and they find their own things to play with. If we take them into our room at night, we try to make sure to have a scratch post, and some other random toys. They sell toys that can suction cup to your wall, that maybe your kitten can play with so it doesn't bother you while you sleep?
Joey was SO playful when we got him, I worried he would never want to be around us. He is such a big baby/lapcat and he is only 6 months old. He runs up to me all the time and leaps onto my lap and purrs so loud and he waits outside the bathroom for me also

Toby, our youngest, we also call BITEY. He is awful with biting. To the point that it is hard to hold him without him biting. So we end up holding him and trying to dangle toys at him so he knows that biting/scratching is for toys and not us. We also make sure to pet his upper nose/head so he doesnt see hands coming at him as a threat ( as that seems to be when he bites/scratches most).
Be patient with it, she is a baby and just playing. My husband gets a little annoyed with the biting sometimes but I just remind him that its what kittens do and try to redirect the kitten. Also, welcome to the site. I just started posting a couple months back when we got our blind kitten, and I love this site. The people are awesome, and I love being able to discuss my kitties with other people who love kitties!