Unsure Whether I Need a Lip Lift Operation or a Rhinoplasty to Achieve Balance (photo)

First off, you have a great looking face. 

You could improve your lips simply and reliably with filler.  I wouldn't to much else.

If your nose flares/flattens a bit with smiling you could do an internal nasal base reduction via your mouth behind the upper lip.  Your issue, though mild to moderate, does occur after maxillary/midface surgeries (Le Forte) so when I perform these I do a little nasal base reduction via intraoral route (same incision used for the maxillary osteotomies) in anticipation of this.  When you do this transoral route for the base reduction you can incorporate some soft tissue plication of the upper lip where it will bunch up a little and hopefully give you your previous look back, though it's not a definite result.  So you could do all that with no external  incision but I gotta tell ya, you really have a pretty face so keep it as simple and concervative as possible.

Best of luck

Dr. Chase Lay

Oh!  Don't do the lip lift.

I don't think you need a lip lift or rhinoplasty.  You may consider fillers for slightly augmenting the upper lip.  Making it about 20% fuller would look nice and still natural.  A nice result would not make your lips look too big, but slightly fuller.  This will also help with the amount of dental show.