Stye is a kind of acute suppurative infection in sebaceous glands and meibomian gland. The main clinical manifestations are local redness, swelling pain, appear induration and yellow purulent point and so on. If you cry a lot, the infection because of the disorder of the tear gland may cause you get the stye. If you get this, you'd better go to see the doctor and have a check.
No, crying too much won't cause stye. If you crying too much, your eyes may appear red and puffy. But it will recover soon after you stop to cry. It won't cause any eye diseases. But stye is just an infection or inflammation that results of blocked glands within the eyelid. And the you'd better to buy some prescribed medicine from an doctor to cure it.