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?
Nope, happens a lot to me, too. Worst part is that whatever you're accidentally plagiarizing, will immediately sound great and will be really easy to write, because of course, you've listened to it before. And it can be nigh impossible to distinguish between accidental plagiarism and just being in a flow.