I'm about 35 weeks pregnant and I've been having these really ugly leg veins?

Common. Varicose veins are just dilated veins near the skin surface. They are very common during pregnancy. Blame your parents for them, the tendency to get them is genetic. If they are painful, wearing support hose may help and so can ice packs. They will get better or go away after pregnancy but will recur with future pregnancy and as you get older.