I have played this piece a great number of times and there are several things you can do.
First everytime the Rh has a phrase you will notice there is an eight rest . Use this brief moment to relax your hand. Chopin was known for his use of rubato so the piece does not have to me metronomic. You can allow yourself slight inflections of your tempo. Often if you continue at a blazing fast speed without allowing points of relaxation your muscles will build up tension. Plan when you will start soft and rubato and use them as relaxtion points.
Second- no part of your body should be in pain. You should not play through pain. I learned this the hard way. If a part of your hand is hurting that is the part that is working too hard. You want to let other parts of your arm do some of the work. Your wrist should be coming up and down to help phrase the melody and your arm can be used to play the first note of each phrase.
Three- instead of focusing on speed- focus on eveness. Speed is an elusion. Achieve evenness and it will sound faster than what your are actually playing.
Four- listen to recordings of great recordings of this piece and you will hear many of them playing with rubato and not playing the piece exactly as it is written on the page. You should focus on achieving the musicality of what they are doing rather than the speed. When you have the musicality loaded in their focusing on rubato, expression, dynamics , phrasing, rather than speed the music will be more enjoyable to play, listen to, and actually easier.
Thanks for this post!
I think this is gonna help me much.
Well, I worked with my technique since I started this thread. I'm already much better to work with my wrists. I know it, because I feel how my wrist help my fingers to play the notes, and I become much less tired now than before.
And now I'm also doing exacly like you say! I take some pauses in the tempo sometimes, and it makes me relax a bit. Yes, I've heard that other pianoplayers do so sometimes and I think it sounds nice to!
What I didn't know at now, was that I can use my hand to play the first note. That was interesting. I'll try that tomorrow. How shall I think to use my hand?
I may post a new video soon, if anyone can see the different between my technique before and now?

Thanks for your reply!
Carbe