Since hurricane Sandy, a number of New York City hospitals have been scrambling to deal with a sharp increase in patients, forcing them to add shifts of doctors and nurses on overtime, to convert offices and lobbies to use for patients' care, and even, in one case, to go to a local furniture store to buy extra beds. At Beth Israel Medical Center, 11 blocks south of the Bellevue Hospital Center emergency room, which was shuttered because of storm damage, the average number of visits to the E.R. per day has risen to record levels. Visits have increased by 24 percent this November compared with last, and the numbers show no sign of dropping. Hospital admissions have risen 12 percent compared with last November.