Okay, so this might be a little rambling.
It sounds like you need to break the mold and try something really different. Like something that's
only a series of verses, or something with a chorus that changes just a little bit each time, or even just a continuously evolving melody. None of these have to even sound
good, just experiment. Don't worry about releasing them. Sometimes you just gotta make music for yourself.
I don't know how much theory training you have, but with little to none I can definitely see why things would get stale after a while. I always plug
this website where you can take music classes online for free. It's a decent alternative if music school isn't an option. I see that one class,
Fundamentals in Music Theory, begins in July. There are composition lessons on YouTube, as well. Also look up other resources, such as
this series of composer workshops that I discovered today. In short, there are many resources at your disposal, so by all means take advantage of them!
Listen to more music; music you love or even music you plain old dislike. Study it closely. Find out all the individual components that make it
it. Take note of structure, timbre, lyrics,
all of it. Ask what makes it resonate with people, what parts do you enjoy and what others do you not, etc. In my opinion, you can always learn from other songs (even ones in completely different genres). For you, I'd recommend looking up improvisation. I think that'd be a good change of pace. Not just piano or organs, but on any instrument. There's more to music than just structure, after all.
Another thing, if you don't already know about it, look up counterpoint as well. It can go a long way towards giving your music more depth; more "meat" to "chew on". Again, you can find some preliminary courses on YouTube and elsewhere. There are various kinds (known as species) and the first kind is actually pretty easy to get the hang of. Then you can work your way towards more complex compositions.
My last point would be to not shun repetition! It can definitely become dull, but if use well it can sound wonderful! Just look up minimalism and tintinnabulation, which are two of my favorite genres. Remember, it's not just what you have, but also how you use it.
I hope some of that could help. I know I spoke in pretty vague terms, so if you want some more specific examples of what I'm talking about, just say watcha need!