Lip Lift or Other Procedures to Make Upper Lip Go Up and Teeth Are Showing?

It would be helpful to see a higher quality photo of just you with nose and chin visible, with mouth slightly open. If your upper teeth are not visible in this view then an upper lip lift may be in your best interest. If your upper teeth are visible and you still want to reduce the upper white lip length then a dental procedure may be necessary as well. 

Thankyou for your question. 
For the look you are trying to achieve, you would need a lip lift not a reduction. To show the teeth as you describe, i would consider a bullhorn lip lift. This places the incision underneath the nose lip junction so the scar is hidden quite well and you can achieve a very nice lift of cupids bow such that the teeth will show in a resting position.
I would defintiely not consider a reduction, as this would pull more of your lip inwards and not achieve the result you desire.
An incision can be placed along the lip margin too but I prefer the bull horn to achieve the look of a pouty lip with the front teeth showing
I hope this is helpful to you
Kind regards