First Time Owner + Kitten

Hi all, I'm a first time cat owner with a few questions.

I got Maple (13 wks, desexed) from a shelter a few days before Christmas. The girlfriend had been wanting a kitten for quite a while, and had looked on the shelter's website and scoped out a few that she wanted/hoped they still had.

When we arrived at the shelter, we looked at two that she'd been considering, and then at Maple (I spotted her). She immediately jumped up on me and nestled into my chest, then started to climb my body and nuzzled into my neck. From then, there was no other choice.

Anyway, we got her home and she actually settled in instantly. No hiding, whimpering, anything. She was so affectionate, sitting on our laps, climbing onto our laptop's keyboards. She slept with us for a few nights without issues (apart from the occasional paw on the face when she was moving around).

Then, around 7-10 days ago, she started urinating on the bed for no reason. Her litterbox was clean and well within "range", and she knew where it was. Blankets changed, next day she did it again. And again. On the fourth time (in as many days) we decided she couldn't sleep with us any more (she did this while we were awake) and was moved to the bathroom.

We let her in a few times while we were in bed watching TV, and she continued to urinate. There was also a bit of a pooping issue once.

Anyway, now she's become really antisocial. I can't pick her up without her squirming out, she doesn't sit on our laps (even when we place her there) and if we try to pat her when she's lying down near us, she'll start to grab our hands with her claws and (fairly gently) bite our hands. Thing is, she'll bite, then lick. But still, antisocial. She darts around the house, last night she totally flipped out, jumped up onto the couch where I was sitting, clawed my leg, sprung off, jumped onto the fireplace guard, ricocheted off onto the Christmas tree, which caused both to topple. This all occured within about two seconds.

Summarized version!
New kitten was super-affectionate, began to urinate on our bed, has been sentenced to sleeping in the bathroom.
Has become antisocial, reckless.
The vet seems to think she's healthy. She's also vaccinated, has been flea'd.

Yeah, she went to the vet for checkup + final vaccination about three days ago, everything was fine. Though she did get a bit lethargic after the injection, the vet said that was normal and she bounced back.

I will definitely try that litter, I really miss having her sleep at the top of my head.
*Edit* I probably should have mentioned that she uses her litter box by herself when the bedroom door is shut or when she's not in there in general. Does this make a difference?

That's if we can get her to sleep there, she's been on a few times (under very close supervision) and has gone nuts, attacking the blanket even when we weren't moving. She did try to pee one of those times, but I saw her scratching at the blanket in that certain way, quickly picked her up and took her to the box, where she uh, went.

I would never give up on her! I'd rather live in a shelter myself than send her back. I've always been an animal person, though mainly with dogs. There have never been any cats in my life.