I'm currently in the process of writing a song. I've got a tune and I'm putting the lyrics together but I'm always concerned that any tune I think of might just be another song I've heard somewhere randomly that I don't remember hearing.
Do I just have a shitty memory or is this a problem that other people have too?
I simply don't think about it. If Chino Moreno can get away with using the chorus chord progression of "Hit Me Baby" in one of his songs and the most that happens is laughter about it in the comment section, it's not an issue.
Alternatively, there is nothing new under the sun. Music has seven fundamental notes that can only be arranged so many different ways and still sound pleasing to the ear. It's an inevitability that somewhere, you're going to use the same chord progressions as thousands if not hundreds of thousands of other composers, you're gonna write the same licks, you're gonna play the same riffs. The difference is in atmosphere, genre, and performance. Don't stress it too much.
Deftones have so much staying power, like they keep making good stuff after 30+ years now. I know Koi no Yokan is like over a decade old, but it's so good, and that was wayyy after their popularity peak.