If I try to play the Revolutionary Etude (Chopin, op. 10, No. 12) fast, my left forearm becomes sore and constrained. I know there must be something not correct in mechanics...
If you would be ready to agree, our fingers do theirs job being guided by our brains... You probably could easier understand my way of thinking. According to this way, the first thing you have to improve is the quality of your hearing, and especially of your anticipative [creative] hearing: let you try to observe how (…if at all?) musical energy actually "moves forward" inside the each particular sound you are taking from the instrument; are your sounds really "alive"? Which is the real quality of the sound you produce on the piano? You must check up if you, maybe, are ready to accept the sounds of such kind you would NEVER accept listening to another pianist...?
The very important point of the matter is the POINT your fingers start to become connected with the keys: what do you feel? Does energy INSIDE of your fingers & hands entirety flows up & to the side (very well!) or purely down (quite bad...!), pushing or beating the keys? Wanting to make your fingers and hands FREE you should not PRESS on the keys, absolutely NOT! You must feel you actually TAKE the sounds UP and make them vivid as well... Doing so, you will get the truly fantastic feeling inside of the hands, just PHYSICALLY, purely sensually. Of course, we should use the weight of all the possible part of a hand (bonuses!), but as well, we must actually operate our hands exactly as violinist operates his right (bowing) hand. The pianists' fingers should AS WELL not press on the keys as the violinists' right hand should NOT press via bow on the strings of the violin. Due to the very mechanical nature of our instrument we still have to complete likely the two, only seemingly contradictory activities at the same time: we must build the musical phrases, which are of the clearly linear character – and complete this VIRTUAL action via the nearly up/down directed motions of the fingers acting in the possible best co-operation with others parts of the hands. Yes indeed, actually the fingers' motions should never been completed via the strictly up/down steered action.
Let you very strongly watch the sound's motion then, from its start up to its end! It would be easier if playing longer, even single sounds, slowly – at the beginning and after then faster and faster, up to the adequate tempo – with the whole will to get such a kind of the inner (virtual) fluency, that will prepare the full and perfect (means: very precise, too) legato. You will quickly notice that the tempo much more depends on your hearing and on your psychical activity then on your fingers' and your hands' action; the fingers' action strictly depends on this all, what just virtually happens in your fantasy and hearing. Of course, the musculature of the hand, which physically moves the fingers, should act perfectly good. Let you believe, only practicing in the proper dynamic ZONE, one would be able to improve the functioning of musculature of his hands. Playing TOO silently (p, pp) you never achieve any positive result in technique. On the other hand forcing the sound could very easily damage your muscles. But, especially in the very first phases of practicing you should rather play louder than too softly.
The entire process of the technical improving could begin only in the case you would never accept any ESTHETICALLY poor sounding result! As Josef Hofmann said, "Great finger technique may be defined as extreme precision and great speed in the action of the fingers" (Piano playing, Dover Publ., 1976, p. 84). I must actually add that such "great speed" should and could be practiced EVEN in the truly slow tempo... You should demand from yours fingers yet they must produce the truly GREAT SOUND, and firstly – in the purely dynamical terms. Of course, let you forget any kind of a heavy drumming and/or banging on the keyboard. It is supposed to be the process of very FRIENDLY bringing sounds to life and ordering them the exceptionally excellent growth...
About fingers now: let you check up the directions of your fingers' motion; I am nearly sure that you press on the keys, just rectilinearly down, toward the keyboard's bottom. At the same time, I suppose, your hand's part – between the shoulder and wrist – is likely unemployed. A "bow" in the hand should steer the fingers, and theirs motion cannot be direct just up and/or down toward the keyboard's surface only! The fingers must act being a little bit turned (pulling by the hand) to that side the melody is actually going on. And after all, they should NOT press on the keyboard’s surface, they should just been dropped down TO THE PROPER level (zone) inside of the keyboard’s depths and as well slightly accelerated in this falling. When tempo would go higher, we would speak about nano-like distances yet. So, bowing, directing the musical sounds' energy up and to the side and hearing, hearing and once again HEARING to the quality of realized sounds – together are shaping the secret of the firm. If the dynamics of realizing music just become even very little too high and this happens out of yours will and control, the hands could feel the first symptoms of the pain very quickly. Let you be very sure about this.