I noticed a big blue vein that runs inside my thigh bulges a tiny bit when i stand but can't see it when lying down. will it become varicose?

Possibly: Family history can contribute to varicose veins, as can pregnancy, and type of activity. Wearing a compression stocking will help reduce this as well as elevating legs when laying down. Persistent bulging, any discomfort, or noting additional bulging veins or other, such as spider veins, etc should be checked out with an ultrasound to rule out underlying reflux or venous insufficiency.

Varicose veins: Yes, it likely will lead to varicose veins. This is likely a prominent great saphenous vein (or a branch off the great saphenous vein) that is under abnormally high venous pressure. This suggests broken vein valves in your leg that are leading to venous hypertension in your leg. Despite your young age, this can occur in young women. Recommend you see a vascular surgeon & get a vein ultrasound.