Hi kind,
Some further explanation:
In piano we speak of "balancing the hands", but that terminology can be a bit misleading to a new pianist, as it implies that the hands should be equally balanced in volume. That, however, is not the case at all. Melody always takes precedence over accompaniment, as goldentone mentioned above. If both hands are equal in volume, then that means accompaniment will compete with melody rather than supporting it, which is not pianistic. Always think of melody as foreground and accompaniment as background.
The best way to balance the hands keeping the right hand (which more often than not carries the melody) dominant while keeping the accompaniment in the left hand subordinate is to think of dynamic levels. Consider the dynamic range: fff, ff, f, mf down to mp, p, pp, and ppp. Suppose that the dymanic indicated in the score is mp. What you cannot do then is play both hands at mp, as the hands (and sound) will not be properly balanced. So you'll instead want to play the melody hand at mp, but the accompaniment at only p. How to do it: The tendency of most is to increase the melody hand to subdue the accompanying hand. It doesn't work! What happens next is that the softer hand rises to compete with the louder hand, which in turn causes the louder hand to become even louder such that the general dynamic escalates. The best approach is counterintuitive, that is, the exact opposite approach. Reduce the volume of the accompanying hand instead and keep it there, allowing the melody to naturally soar above it. Where you're a musician, think of accompanying a singer. Whenever you encounter a cantilena or bel canto line in playing the piano, think voice. It means that the piano cannot drown out the singer. The accompaniment needs to be more refined and subdued. Through touch and articulation, you reduce the accompanying hand (more often than not the left) to tone it down to place it in the background.
Another suggestion: As you continue to play piano, use your ears to keenly monitor your pedaling. Right now you have too few pedal changes and you're getting considerable blurring that's disturbing the clarity of your playing. It's a bit like run-on sentences now. Use syncopated pedaling, that is, as you play a chord, catch it in the pedal a nanosecond after it sounds and before you release the hand from having depressed the chord, rather than pedaling chords simultaneously as you play them. If the chords remain the same without causing dissonance, you can keep the damper pedal depressed. But if there are changes in tonal center, or passage work with neighboring and passing tones, more pedal changes will be needed to keep the sound clean. In some instances, no pedal at all is the best solution. In the repertoire you're playing now, much of the pedaling will be indicated to guide you. As you you advance, you'll find that composers indicate less about pedaling and sometimes make no indications. So developing pedaling techniques consistent with performance practices in the styles of the musical periods will be very important. For example, pedaling techniques for Debussy will not be transferable to Haydn.
Having mentioned those two things, I want to compliment you on your playing. You mentioned the other instruments you play, and I believe that you show your musicianship in undertaking piano--even after this very brief amount of time. For that reason, you're already showing some musicality at the piano. Stick with it! Even though you're starting piano relatively late, my sense is that you have fine potential.
Topic: Chopin's Waltz in A Minor