Are There Plastic Surgeons Who Work with Adults with Cleft Lip?

Most plastic surgeons, facial plastic surgeons (ENT), and pediatric surgeons are trained to do cleft lip, palate, and nose surgery, but not all continue to do them in their practices. Those that do ultimately gain experience in doing both lip and nose revisions, as their young patients' growth can cause unexpected changes in previously-operated areas. Some of these changes require surgical revision(s).

Now that adult age has been reached, changes are no longer occurring in your lip and/or nose. Prior surgery causes scar tissue, and the more there is, the more difficult the revision. (It may even be lucky that you didn't have a third surgery at age 12!) Hopefully, the initial surgeon(s) preserved as much tissue as possible, and now repositioning and adjustment with skilled technique and fine sutures will yield a better result. Each patient has uniques needs and previous scars, though yours (by looking at your photograph) seem fairly common.

Seek an experienced, board-certified plastic surgeon or facial plastic surgeon who continues to do clefts either in their everyday practice, or who has extensive experience in doing charity cleft surgery overseas. In my opinion, he or she should also have at least a decade of rhinoplasty experience, and continue to do lots of these surgeries in their regular practice. As an adult, you would no longer be a candidate for secondary surgery by a pediatric surgeon.

Cleft rhinoplasty is a challenging operation. I often will revise the lip at the same time as the scar can be advanced to make the nostrils more symmetric. I recommend seeing a surgeon who both performs a high volume of rhinoplasty and cleft surgeries. 

Cleft lip and palate can cause a series of problems for patients as they grow and mature even after the initial repair.  Kids with cleft lip and palate as the grow can have more issues with recurrent ear infections than most other kids and often require ear tubes throughout their childhood.  The development of adult teeth can be disrupted requiring tooth extractions, bone grafting and dental implants. 
As kids reach adolescence , they may notice changes in the shape of their nose that bother them both in appearance and their ability to breathe through their nose.  In the typical unilateral cleft lip, the septum is often deviated to the non cleft side, and the nasal tip is not well supported so it can tend to droop.  Also the nostril on the cleft side may appear widened, and collapsed because the insertion point of the nostril is further back and down than the other side.  Commonly in kids born with cleft lip who have had a repair of the lip as a baby, they may require a septorhinoplasty to correct these issues.  Because of inadequate cartilage to support the tip of the nose, many times these surgery can be more complex than the average rhinoplasty requiring cartilage grafts from the rib or ear to help reconstruct the nose. 
Lip asymmetries and scarring can become bothersome as well which may be the result of the severity of the original cleft deformity, the original reconstruction surgery, or the patient's body's healing and scarring.  Scar revision of cleft lip repair is not uncommon as well and can be done at the same time as a cleft rhinoplasty.  
Make sure you consult with a trained and certified facial plastic surgeon or plastic surgeon who you feel comfortable with and is able to explain to you their plans and recommendations.