Question about getting curly/flowy hair?

I have had my hair relaxed ever since I was young so that it made my hair straight. Recently, I have really been wanting to change my hair so that is curly (not necessarily like an afro, but just curls that fall on the shoulders). I went to a stylist and she managed to do a twist out while using a texturizer, which I liked. Only after 3 days though, my hair went back to being straight due to being combed out. I was wondering, is there a way to permanently make African American hair curly?

Also, my hair sticks straight out instead of laying flat down, and I was wondering if there was a way to have it lay flat on my shoulders with flow?

Example of what my hair looks like: https://prnt.sc/o5g16t

What I would like my hair to look like: https://prnt.sc/o7q9z9

Edited by thenerdcat - June 27 2019 at 10:41pm