Is exercise the only thing that makes your heart beat faster?

Yes because when muscles are used for exercise or anything they must be replenished with oxygen, nutrients, etc. They also produce waste products that need to be taken away from the cells. Blood is the transport system for all of these things so the harder your muscles are worked the quicker they burn through nutrients and produce waste meaning that the blood must flow faster to provide all of this, the only way for blood to flow faster is for you heart to beat faster.