I'm guessing you have 2 separate reservations: one for 31 Dec for 1 (free) night and another for 1 Jan for another (paid) night. The second will obviously count for 2017, and the only thing I could suggest is to visit the front desk some time on the 1st to "check out" of the 1st reservation and check in for the 2nd.
Thanks! Good idea about checking out and checking back in. I will be up early for breakfast anyway so I will do just that so I can have peace of mind.