What procedure would allow me to show more teeth when I smile and speak? (photos)

There are surgical and non-surgical approaches to lip augmentation. Non-surgical approaches include botox (slight lift, reducing gum show) and filler (volume restoration). Surgically, you can have two separate incisions under the nose (italian), one incision under the nose (bull horn), one incision at the red/white upper lip junction (gull wing) or two separate incision at the corners, or a combination, depending on your desired look and anatomy. My preferred surgical technique is called the Elelyft, which is a version of the bullhorn approach. 
The ideal candidate for the Elelyft, or upper lip lift, is someone with a philtral length of 13mm or longer, no upper dental show, and/or a thin upper lip. The nasal base to mouth width ratio needs to be taken into consideration to avoid leaving the lip corners down.In your situation, to expose more of the upper teeth, a lip lift would be best for a long lasting result. Please review before/afters and my lip lift information page is quite detailed. Consult with an experienced lip surgeon for a complete range of options that are appropriate for your situation.
Gary Linkov, MD
Lip Specialist
Manhattan

You had botox to relax the lower lip?  That's not going to be effective for lifting your lip.  And, botox for the upper lip will almost always make that longer too.You attached three photos, but the key photo is to see your mouth open with your face relaxed.Probably you need a lip lift. This is done in the office and takes about thirty minutes.The link takes you to one of several articles I've written on the subject.