Dealing with angriness or sadness that comes up with "meditation"
How to deal with it without being ashamed of such feelings?

There's nothing wrong with feeling shame. How to deal with it? From a Buddhist point of view, you should practice meditation, and in my opinion, Vipassana meditation. 

By doing so you will come to terms with these feelings as they arise and they will no longer effect you in such a way, and by the sound if it, you will also be able to come to terms with this aversion you've built up to the intense experiences of pain you had in the past, which may have had some role to play in leading to your present experiences of anger and depression.

Here is a brief article on pain and how meditation can help you come to terms with it: http://www.shinzen.org/Articles/artPain.pdf

And here is a good talk from a Buddhist point of view on the experience of pain and how it can be useful for us: https://www.youtube.com/watch?v=BldDclolLCg

In any case, I would suggest you shift your focus from the healing of your knee, to the healing of your mind, as that is where both these negative emotions are arising, and the suffering from the pain in your knee. We dont always have a choice in experiencing pain, but suffering because of it is a choice. Best of luck.