The peach tree paradox (not a poem)

This is a time paradox I came up with.
It's probably similar to another one, I haven't checked.
Just something stupid to keep you occupied if you're bored.

Say you have a peach tree and it's the last day of ripe peaches.
You pick the peaches off the tree.
Then you jump in your time machine and go back to yesterday, the penultimate day of ripe peaches.
You pick those peaches.
Then you go back to the future, would you have the first batch of peaches?
You couldn't have picked them.
But you did?
So do you keep only any peaches from the previous days?
Or do you keep creating new parallel time lines?
I think parallel time lines is correct, though it's a frustrating conclusion.
The more days you'd add more parallels
And you'd have to start in a new time line because old time line peaches are gone?

I'm hoping someone has a better answer.