I was frustrated when first writing songs that they all sounded the same. Of course, I only knew one key, and I had a limited number of harmonic moves to deploy. In retrospect, though, it makes sense to develop the same material in three or four different ways before moving on to something else. I've continued to do that: I find an idea, melodic or harmonic, and use it for at least two songs.
Having a style, then, having one's songs (or poems or scholarly essays) sound like one's self is not at all a bad thing. I'm wondering why I thought this was even a problem. Style stems from limitations (or more positively the finite number of things within one's repertoire) and from a set of preferences, what one wants to do in the first place. (For example, my use of "one" in this post is irritating to me. It is not my normal preference at all, but I just fell into it. But it is not discontinuous with my style, either, just an added wrinkle. The post still sounds like me.)
Each chord has a color. Yet all my songs together, composed of different chords, have a kind of coloration. Not a single hue, but a composite range of tones. I am weirdly proud that I can do this at all.