Distortion and Curving

hello there! 

I'm a rookie to photoshop and I wanted to almost curve a photo similar to an artist's technique for a school project. However, I'm not quiet sure how to do it and searched for some tutorials online. 

I've tried using some distortions through filters however, its not making me satisfied... I came here in hopes for someone to help me 🙂 I have the image of reference and the photograph I'd like to edit.