Yale went to the vet today, and got fully checked out. We took X-rays, and it's nearly certain there is nothing broken. It can be a little hard to tell, with kittens this small, but the vet feels confident, and so do we.
Instead, the vet supposes that Yale probably has feline calicivirus. If you look that up online, you should know, it's probably not as scary as it sounds. A great lot of cats have it and are just fine. Typically they'll get sick for a while, fight it off, and then just live with the virus, and no real symptoms -- and no further chance of contagion. That's what we expect for Yale. And we don't have to worry about Yale infecting any of the rest of the Faculty, because they're all vaccinated against it already. Most cats get vaccinated against it as a matter of course.
Of course, while the vet's diagnosis is almost certainly correct, it's also worth remembering that we didn't perform and real test for calicivirus; it's a presumptive diagnosis. Whenever you have a kitten that has a fever and a limp, this is what you assume is going on. Because it's likely, and common. We'll be 'treating' it by giving her some powerful painkillers to help her get by, and some antibiotics to help prevent any secondary infections.
Then we just wait for her own immune system to fight it off. Which is almost certainly how it'll go. No worries!