I am not an expert pianist, but my brother is, and he is also an instructor in piano technique. As his student, and from my own experience with this, I would offer the following observations:
Let's get into more detail with the relaxation concept. What does that really mean? Frequently when playing, if you pay attention to the way your hand feels, you will realize that you are holding your hand stiffly in a set position, or holding your hand in a particular shape. Why would you do that? I would suggest that we pianists do this as a (misguided) means to obtain more control over our technique (could be volume, touch, tone, or other objectives). Also, pianists frequently hold shapes with their hands because they feel more confident about hitting the correct notes if they force their fingers to line up with the shape of the musical passage. These types of activities are both unnecessary (in my experience) and even harmful. It is one thing for tension to arise because you are performing an activity with your finger, it is another if you have tension in your hand before you even touch the keyboard. How to address this? Some suggestions off the top of my head: Before you touch the keyboard, allow your hand to take it's neutral position. Hold your forearm out straight, and let your hand droop freely. Then, slowly extend the fingers just enough (and no more) to allow you to play the chord of interest. Keep the fingers that you are not using relaxed. Gently lift up unused fingers with your other hand while holding the chord to see if they are actually relaxed. For passages that move rapidly (as opposed to repeated chords), you need to learn to relax your fingers after releasing notes. In other words, after releasing a note, allow the finger to return to its neutral position and only stretch it out again when necessary. You will have to pay close attention to these things for a while. Stop frequently in middle of passages and check that your wrist and hand do not have tension.
These relaxation techniques may not be enough, however, because there are some larger fundamental problems. One of these is lack of efficiency. If you are playing forceful and/or loud music, you need to learn how to produce volume without excessive strain. Volume comes from the speed with which the note is pressed, NOT the forcefulness of it!! (not the energy, not the weight, not the pounding, not the heaviness). You need to move through the note with acceleration to achieve volume efficiently.
But wait, that still may not be enough. You may be working your fingers too much. If your fingers are doing most or all of the work, then you will get all of the stiffness, soreness and other issues that accompany highly repetitive muscle exertion (performed near the limits of strength and with fine control achieved through tensing opposing muscle groups). With practice, you will be able to play longer before these issues set in, but I am not sure that is particularly advisable. What you need is to offload some of this effort to muscles with much greater strength, namely your arms. If you learn the Russian Piano Technique, for example, you will find that most of the force in playing originates in the arms, and is based on the fine control of arm weight. Your fingers can then be relegated to the duty of acting as extensions of the arms, so to speak. In my experience, with a technique like this, strain in the fingers and wrist is dramatically reduced. Also, control, sensitivity, and consistency all improve.
The musical world is awash in mediocre (but serviceable) technique. Piano teachers frequently suggest poor hand form and other mistaken approaches. Find a teacher, if you can, who has a deep understanding of the nature of piano technique. Most casual teachers do not. Many are considered qualified merely because they have been playing piano a long time. Experience is of course valuable, but it does not always confer true expertise. At the very least, such teachers may be unequal to the task of addressing thorny questions like this because even if they have solved these problems through experience, they don't actually know why/how they solved them, and hence they cannot really help you. Listen to your body, and avoid advice whose central premise is that working through pain or practicing excessively is the solution.
Best of luck!