The best treatment for veins of the face is a laser, I would not consider sclerotherapy on the face for fear of scarring.
I would definitely recommend laser treatment for the telangiectasia under your lip. Given the size and location of the lesion, laser will give you a very nice result. Specifically, a pulsed dye laser or 532nm KTP laser would be most effective. You can expect a small amount of swelling and there is a possibility of a small purplish bruise in this area which will resolve within a week. You can cover this area with concealer make up if you desire after treatment. Best wishes.