Will lip injections fix my turtle lip? (Photo)

I have thin lips and I'm looking into Injections I have a really defined Cupid's bow and it comes to a point and i look like a turtle when Im not smiling. The point on my lip hangs over my bottom lip, I want to be able to have a nice full lips even when I have a resting face. I had an accident when I was younger and had to get stitches on my top lip, I'm not sure if this is why my lip looks like this, it happened a really long time ago but, I'm worried if I get injections my lips will look weird.