I would never presume that we have the same knee problems, but I have had knee pain that sounds similar to yours. In my case, instability in my foot-ankle-knee allows the knee to wander towards the body centerline under heavy stresses, pulling the kneecap outwards where if rubs on the sharp edges of the femur (or is it tibia?). The simple fix was proper wedges under my cycling cleats and orthotics in other shoes, along with a lot of conscious training to keep good form (knee stability) when exercising.
Have a speedy recovery!
The Movement-Exercise-Analgesics-Treatments protocol is a recognized alternative with some promising support in early studies.
A nice comparison can be found here: [http://www.thesportsphysiotherapist.com/rice-or-meat-protocol-for-acute-ligament-sprain-treatment/]
From the article:
"REST – Whilst rest should more accurately be taken as ‘Relative Rest’, some take this to the extreme. Complete rest would be disadvantageous for the treatment of most acute soft tissue injuries."
"The RICE protocol hampers soft tissue healing, whereas MEAT encourages healing"
To be clear - I am NOT advocating walking off a badly sprained ankle. Just saying that in a case like Larry's a little activity is likely beneficial, and, after identifying the cause of the problem, significant (but controlled and sensible) activity may well be best.