When I Smile or Talk, You Can't See my Upper Teeth. How can this be corrected? Lip lift? (photo)

Your problem is that you have an underdeveloped midface, and specifically an underdeveloped maxilla.  The teeth and bones of the maxilla support the facial tissues.   Your maxilla is set back and narrow so it traps your lower jaw as well. 
This is a developmental issue not a genetic issue.  Ideally maxillary expansion iis done before age 7 and as early as three.  Allergies and not being breast fed can contribute to the problem as can tongue ties.
The deep nasolabial grooves are do to insufficient support and when we do see teeth in the pictures there are dark buccal corridors.
Narrow maxillas correspond to narrow nasal airways and  frequently dark circles under the eyes.  This is made worse if orthodontics includes bicuspid extractions.
Avoid plastic surgery which will ignore the foundational issues.  Orthognathic surgery by an Oral Surgeon is a possibility moving the maxilla downward and forward.  Crime shows like CSI or Bones look at a skull and then build a soft tissue face over it.  The hard foundation supports the soft tissue and look of the face.  
Tou are also over-closed and have a short lower third of the face causing frown lines or possibly making people think you are sad or angry.
Dark circles under the eyes and forward head posture are common along wiith TMJ disorders, headaches and migraines.
The best approach is to correct the underlying orthopedic issues by 3 dimensionally growing your maxilla and mandible with the DNA Appliance rather than surgery.  This will also correct the nasal airway and associated issues.
If you snore or have sleep apnea you may want to consiider the RNA version of the DNA Appliance that can treat and in some cases cure sleep apnea.
The  web reference has multiple patient videos on use of DNA Appliance.
It is possible to do a full mouth neuromuscular reconstruction to do a dental facelift by build the smile out 3 dimensionally with dental  crowns and veneers.  This can typically cost 40-70 thousand dollars.  This is a fast way to correct the full mouth smile and bite issues.   
A diagnostic work up and trial period should precede this type of permanent work!

It looks like there is deficient maxillary(upper jaw ) growth. This could be corrected with surgery( maxillary re positioning or lefort) and the appliance may have some benefit. Alternatively it looks like you have over 100% overbite where you do not show your bottom tooth to do possibly wear. which also causes your resting reverse smile line. Using crown and bridge to increase the distance between the two jaws could address your smile, add length and show teeth when you smile and are at rest. Typically at least one arch, ideally both are prepared at the same time to address the issue.