Lips turned in. Do I need a lip lift to achieve my desire result? (photos)

I dont know if you can tell by the photo, its hard to explain, but its like some of my lips are like hiding in my mouth. when i simply push up the sides of the area above my lips, it reveals it. I want a permanent version of this, ive looked into a ‘lip lift’ but it seems like that procedure kind of targets the middle of the lips? while im trying to raise up the sides like i did in the photo. will a lip lift give me the results i want, or is there a different procedure?