If a contact lens runs into the top of the black eye, where the conjunctival sac of the upper lid is located, it is often difficult to remove it at home on your own. Usually, the harder you drill, the deeper it may go, and the more damage it may cause to the eye. It is generally recommended to go to a hospital, especially to have the lens removed by a doctor under a slit-lamp microscope. Usually, the doctor will open the eyelid to find the location of the contact lens, and then use a cotton swab or tweezers to remove the lens completely. Such a procedure does not damage the cornea and the relative sterility of the procedure reduces the risk of eye infection. So if this is the case, then going to the hospital is the safest way to proceed.