I'm 20 years old. I'm on birthcontrol and have been on it for years. I have varicose veins. If I had a blood clot, would majority of my leg be swollen or red?

Swelling sometimes. You are female, 20 years old and have vericose veins. You are taking birth control pills and are concerned about deep vein thrombosis (dvt). If you have a DVT sometimes the leg gets swollen and/or may become tender. Your doctor can order a noninvasive test to look at the deep veins of the legs for a dvt. Vericose vein are in the superficial veins so are not dvt.
Not necessarily. There are two kinds of blood clots that can form in the legs-superficial and deep. Superficial usually occurs in varicose veins and is easy to feel and tender with redness. The swelling is just around the clotted vein. Deep clots are deep in the leg, harder to diagnose and associated with leg swelling. Since you have vv and are on bcp's, it would be prudent to see a vein specialist.
Veins. In general superficial varicose veins if clotted were present with swelling, as well as redness over the track of the varicose vein. There also may be associated swelling. There is a relationship between use of birth control pills and possible venous thrombosis. If you are suspicious, I would urge that she will be evaluated with a venous Doppler-sonogram as soon as possible.