We took Sasha to the vet yesterday. It wasn't too bad! Fortunately, there were no surprises. Meaning that her only issues were the upper respiratory infection and ear mites. Her blood work was negative and they didn't see anything in her fecal sample, although they did deworm her just to be safe. We brought home some antibiotics for her infection and once it starts having an effect we'll take Sasha back to the vet and start getting her vaccinated.
Also, the vet confirmed that she is a girl and she's around 3 1/2 months old. The vet gave her the arbitrary birthday of February 7, which will be easy to remember because I just so happen to have a cousin with that birthday.
ETA: I gave Sasha her first dose of medicine this morning (via a dropper). A good bit of it ended up on the side of her mouth, but I'm certain at least half of it went in. I'm pretty proud of myself. And she doesn't hate me. Since cats can hold a grudge I wasn't sure if she'd come to me after I was done, but she's still lovin' on me.