Can getting upset about something cause tachycardia?

YES!!: Of course it can. Not enough information to truly answer your question.

A Racing Heart: One's emotions often manifest as physical symptoms. This is known as a psychosomatic response. When you are upset or angry your body can initiate a "flight or fright" response during which time you experience tachycardia or rapid heart rate. As you resolve your reason for being upset your heart rate returns to normal.

Yes: Stress, anger, etc., starts the body's sympathetic nervous system response. This includes release of adrenaline, higher heart rate, faster breathing, elevation of bp. Some people get arrhythmia when stressed. Breathe deep and relax and things should go back to normal.