You will have the terms and conditions on your booking confirmation. It is most likely that EITHER you have the option of cancelling without penalty AND the hotel has the option of changing the rates OR the booking is mutually binding on both of you ie it is unlikely to be binding on one side at the rate and not the other side. Quite often their is a third option and that is that you have the option to cancel but the hotel guarantees the rates.

The word guarantee might mean they guarantee to give you a room (but even then it might mean that only if one is available when you check in) or it might mean that the price is guaranteed. If it isn't clear, it is reasonable to assume that the meaning is in the hotel's interest and not yours, unless you have the stomach to seek the option of my learned M'lud.

It is the terms and conditions you need to look at as no one here can help you or give you any definitive answer without knowing what they say.