Just about everything you've ever heard will return as snippets in any subsequent writing. Could say it's like shingles - it's in there waiting for a trigger, and off it goes!
The trick is to use these bits of music but be very careful that they remain as only bits. I dare say that if you studied 100 pieces of music, there would be similarities of runs of maybe 3 or 4 notes in some, even down to the timing. It's only plagiarism when it's done on purpose (except in George Harrison's case!), and as long as you are aware it's happening, you can change things subtlely, but I bet that whatever it gets changed to will resemble something else. Something else that you may not even be aware of, or even aware that you've heard it before!
A change of rhythm or harmony in a tune will render it rather different, so there's something to experiment with, too. A little idea. Take someting like 'Three Blind Mice', or another well-known kids' song. Keep the same notes in the same order, just change the rhythm or timing of them. Voila, a different tune.