The word you are looking for is 시리다, meaning chilly or achingly/painfully cold. Rather than cold pain where cold complements and characterizes the pain, this one is the other way round: it is more directly about the cold that is characterized by pain. 시릴 수 있어요 would, as you might expect, mean It might get painfully cold. The word is usually used to describe sensations of parts of the body, often in contact with something cold, e.g. teeth. Since you can't find it in a dictionary, here's an entry on Naver Dictionary.