I have severe pain in my left foot on the left side outside of foot, veins swollen, sudden severe pain that happened for no apparent reason. Even hurts when touched. No swelling.?

Trauma? If no injury involved, i would get seen asap by your local podiatrist or family doc.
It is plausible . You have a clot in one of the veins in the foot. Because, the pain is severe and no trauma, i would visit a podiatrist.