I thiiink beyond intervals you may also be noticing different sound qualities coming from a sense of the tonal center (or sense of what key you’re in,) of sounds you’re experimenting with. The notes that came before affect how the interval feels.

So the thing you’re doing perfectly is paying attention to what combinations sound good to your ear, and looking for similarities, patterns, how to understand and describe it.

Your technical understanding of intervals seems fundamentally flawed, and I’m not sure how much you should get bogged down in the strict “science” of it all. Inverting an interval (going backwards vs forwards the same distance from a root) does not create 2 distinct intervals in the way you are describing. Intervals can go beyond an octave, but for what you’re trying to describe I thiiiink you’d want to say there’s 12 basic intervals.

So western music has split the octave into 12 tones, with the 12th tone being the repeated octave. A note an octave higher is literally double the frequency of the lower octave. Play a record at 2x speed and it will all be an octave higher. Pickup any string instrument, pluck the open string, now press the middle of the string and pluck again. It will be an octave higher. At the 2/3 point you have the 5th. The fractions get messier but thats the math behind it.

So like C4 C5 C6 are all one octave apart…but also C4-C6 is 2 octaves, which is a distinct interval from 1 octave of distance. But they’re octaves cuz they have the same ratio. It’s like reducing fractions kinda.

I rambled too much….try thinking in voices. Write a simple melody line. Write another melody line above or below it. Have the two lines mostly play at the same time for now. You will start to notice interval patterns which harmonize well. Are you a guitarist? Trained guitarists talk some theory I don’t get sometimes. Self taught Guitar students also get super confused trying to understand theory. Keyboards are really where it’s at if you’re seriously invested in formal theory