It could be lots of things. You need to see an orthopedic surgeon to be checked out. They should do an MRI and other tests to verify. Could be an injury, could be an autoimmune problem. Can't say just from knees burning.
I am not a dr. My statements are based on years of experience and related education. Consult with the professional of your choice regarding matters of concern.
I've had long time issues with muscles and neurological symptoms. I agree with Robert that you should see a doctor and see if they can figure it out. In my case, I do a lot of reading about alternative treatments. Burning pain in my experience has always been neurological. It would feel like just the surface of the skin was burning. I had a lot of tests and medications were suggested to me, but I avoid medications unless a last resort. I read that a shortage of magnesium can sometimes either trigger this or make an underlying issue worse. So I looked up what foods had magnesium in them - - nuts and seeds and green leafy vegetables. All foods I had not been eating. So I spent the next two days eating tons of all of those at every meal and 6 months of burning pain started to diminish. After 3 weeks it was all gone. I was very fortunate to have such a great result. It rarely happens that way. I do have an underlying condition that makes me vulnerable to neurological pain, so I don't mean to suggest that simply a lack of magnesium would cause it, but it did relieve it. So I always suggest it to anyone experiencing what might be neurological pain, because it is very easy to try and won't complicate things like a drug might.