There is a kind of paralysis that some people get where they wake up in the morning and can't move (it's what keeps us from flailing around during dreams). It also only lasts a few minutes. Wondering if it can be partial paralysis in your case? I have woken up with an arm that I couldn't move due to lack of circulation, but it was cold. Also, as the circulation comes back, it tingles and hurts.
I just woke up and my brain is still asleep, lol, so I can't remember the name of the paralysis upon waking. When I think of it, I'll edit my post so you can look it up, unless someone else lets you know first.
Also, you can get "silent migraines" where you don't feel head pain. My daughter has had them for years, even to the point where she's nauseated and throwing up. Arms (and lips and face), can go numb with migraines, but I've never heard of it with knees, though that doesn't mean it can't happen.
Please test your legs before getting out of bed, or hold on to something so you don't get hurt, and get to a doctor!
Edit: I looked it up and it is sleep paralysis. It affects quite a few people, and, in some instances, it can actually be caused by some medications. I couldn't find anything on partial paralysis, though, so it might not have anything to do with what you are going through.
Second Edit: Just found something about "paralysis of only one limb" in sleep paralysis. You might ask your doctor about this.