Can a Crown Become Loose? If So, Would It Need to Be Removed and Re-cemented? Would I Need a Root Canal?

My crown is about a year old. It started becoming sensitive to cold and hot recently. It's more sensitive to cold. In fact, putting a hot towel on my jaw seems to help. But eating hot food directly does cause some pain (not as much as cold). When I put my tongue over it in the back, it sort of feels unstable or loose. I'm afraid to go back to my dentist since he's the one who did it in the first place. I did have brief sharp pain a couple months ago when I got work done on tooth next to it.