How can I fix the dark lines that curve down from my lips? I am willing to try anything it's a huge insecurity. (Photo)

Those lines can be improved with strategic injections of filler. These lines can be directed more horizontally. To see how it would look, you can try a short acting filler, like Belotero. If it looks good you can use a longer acting filler.

In my practice, I try to stay away from these combination regimens, as cortisones are non-selective inhibitors of melanocytes.  I would recommend my patients to start Melarase AM and Melarase PM for the pigmentation.
I would start with an intense skin rejuvenation protocol for age spots that includes fractional laser, Covalent chemical peels, and daily skin brightening creams to improve your skin’s complexion. Laser therapy, he adds, must be combined with a proper skin regimen to enhance and maintain youthful results.
He recommends the following skincare products for dark age spots: Melarase
MelaClenz Brightening CleanserMelarase AM: Day-time skin lightener with SPF 30Melarase PM: Night-time skin lightenerMelapads: Daily Exfoliating PadsReplenish Retinoid Cream: Exfoliating and skin-stimulating night creamBest, 
Dr. Karamanoukian
Realself100 Surgeon