My Lipstick Bleeds into my Vertical Tiny Lip Lines - What Can Fix This?

I am in dire need of filler treatment for the fine vertical lines around my mouth. Or else I need to find a lipstick that does not "bleed" into the tiny lines! I have tried lip liner and that does not work - the lip liner bleeds also. What fillers are good for these wrinkles and how long can I expect the treatment to last?

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