Would exercising help to get rid of varicose veins?

Exercising will cause more stress on the veins in your legs and will likely cause them to increase in size rather than eliminate them. It is "blood pumping" that caused them in the first place. There are non-surgical treatments but as they also depend on drugs combined with constrictive support hosiery (elastic stockings) they are not popular among young women. Save up your money and go for private surgery.