Is it possible to suddenly be lactose intolerant when I wasn't before?

Yes but... Lactose intolerance can present later in life for a number of reasons, including intestinal injury due to viral illness or other problems. However, before you give up ice cream, you need to be carefully evaluated as other things like inflammatory bowel disease (crohn's disease, ulcerative colitis, etc) can produce similar symptoms. See your doc for a thorough exam and work-up.