Tearing is the most nature way to moist your eyes. Even if you wear contact lenses, the tears can moist your eyes. So, it is Ok to cry with contact lenses. But if you cry too much, the amount of tears may flush your contact lenses out or the amounts of tears can make your vision blur with contact lenses. Anyway, hope you will be back and forget some awful thing soon.
Crying for a long time will result in a slight degree of injury. Tears itself can play a lubricating role, But once contact lenses are fully lubricated, those will slide out the right range to wear. So you have to make it back into place, after a few times the surface of the white eyeball will suffer different degrees of slip injury.