Birth Control and Deep Vein Thrombosis?

I started birth control about 4 months ago. The first month I was on the nuva ring and my vericose veins were sore, but not showing above the skin. I was only on the nuva ring for a month, then I switched to Yasmin and my vericose veins are going haywire! My white legs look like someone took a blue crayon a drew on them. I want to stay on birth control, but I need one that doesn't have as serious side effects! My dad died unexpectedly from a P.E. last year and I don't want to be another statistic. What birth control would be the safest with my DVT? Serious answers only please?