ok, still please take this advice with a grain of salt because I'm only hypothosizing about what you may be doing.. Please also understand that what i'm going to advise is a RUSHED explanation and there is more information required, and the motion needs to be very refined for you to play at speed and with control.
Your likely not rotating the forearm and therefore placing loads of stress on your extensor/flexor muscles trying to get your fingers up and down at speed.
You may also be twisting the wrist to the left while playing, putting tension into your wrist and down the left side of your forearm.
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Look at your hand. let it sit naturally aligned with your arm, you'll see that you're little finger is further ahead than you're thumb. Sit it like that at the piano, as in, don't twist your wrist to the left so that you're little finger and thumb sit in a paralell line with the keyboard. Instead let the thumb sit closer to the edge of the keys and the little finger sit further in toward the black keys. You should be able to feel whats comfortable.
Now, take your hand off the keys, away from the piano but hold it as if you are sitting with it over the keys. Rotate you're forearm from the elbow.. see how you can turn you're hand from palm up to palm down. This places no strain on any muscles that move the fingers. Refine the motion so that you can do very small left/right rotations with your palm facing down. Now go play the notes like that instead of using your fingers.
In reality you're fingers will still need to move, but they will now be supported by the arm motion, dramatically reducing the impact on the flexors (fingers down) and almost completely reducing the impact on the extensors (fingers up).
If you try this and find that you still feel discomfort don't continue practicing, come back and explain what you tried and what discomfort you are feeling. If you don't get it quite right you may find that you fix the discomfort in your hand, but find you have a new discomfort somewhere else.
Hope this helps atleast a little, good luck.