I have varicose veins and after I have sex if I stand on my feet for awhile (cleaning or cooking) my leg starts to hurt very bad. Why is this?

Venous reflux. U need to have a venous "reflux" study as you sound as if the greater saphenous vein (at the junction of the femoral vein) is incompetent or exhibits relfux..
Valvular reflux. Varicose veins worsen when standing and lessen when supine or lying. This is due to the underlying cause of varicose veins which is malfunctioning of the valves in the saphenous system. When you are upright, the venous pressure builds up in the veins, the valves reflux and blood flows backwards resulting in increased venous back pressure. You should see a vein specialist for a venous reflux exam.
Strange! It is not common for 25-year-olds to have varicose veins, nor is it common for them to hurt. If you have had one-sided leg pain and swelling, you could have a blood clot and may need to have it checked out. One quickie answer would be to try advil (ibuprofen) 600mg prior to sex and to wear compression stockings always. Not the most appealing, i know, but you need to stop the progression. Also, find the cause!
Gravity, pressure. Varicose veins swell when you stand on your feet and gravity draws blood into them over time. They swell after sex because vigorous activity may increase the pressure in your chest and abdomen while your blood vessels in your body are dilated due to the various hormones circulating at the time. These are both normal for varicose veins. Have your veins removed by a specialist , a phlebologist.
High vein pressure. Varicose veins are caused by incompetent valves between part of your superficial leg veins (varicose) to deep veins. Thus, through incompetent connection (valve/valves), blood from deep vein is entering surface vein opposite normal flow direction. Varicose veins accumulate pressure in lower parts of legs & can cause pain & skin changes. Vulvar varicose veins can cause intercourse pain. Treatable.