Botox can help soften vertical lines on your upper lip, but must be applied in small doses to avoid difficulties drinking from straw or a glass. You can also soften those vertical lines with micro-needleling treatments.
A photo would be helpful to understand your concerns and a physical examination to see how the muscle effects the area is also important. A small amount of Botox can be used for over active muscles and filler material (I tend to use Belotero in this location as it can be injected more superficially), but both of these are temporary.Laser resurfacing or dermabrasion is a more aggressive and more permanent method of removing the lines, but does require some recovery or "downtime".A really nice intermediate treatment is collagen induction with microneedling (I like the Dermapen for it's variable adjusted depth and oscillating frequencies). This takes a series of treatments about 3-4 weeks apart, but only a day of downtime. It helps your skin rebuild and replace the lost collagen while improving skin tone and texture.