Tachycardia is technically any heart rate greater than 100 BPM. It doesn't necessarily mean that the heart is not pumping enough. What can happen with an elevated heart rate is that the heart doesn't have enough time between beats to fill properly, resulting in decreased stroke volume and cardiac output, but this is typically only seen clinically with certain dysrythmias that have very high rates (like in the 150-200 rage), or in the setting of cardiomyopathies (diseases of the heart muscle), MI (heart attack), or heart failure. If your heart muscle tissue was actually not able to keep up, it would mean you had one of these things, which you most likely didn't.

What you are describing sounds like textbook palpitations. It is completely normal for the heart rate to increase for a lot of reasons, including stress and being startled (via the sympathetic nervous system, or fight-or-flight response). A palpitation is when a person becomes very aware of their heartbeat and perceives it to be abnormal, regardless of whether there is any clinically objective abnormality. They are often associated with anxiety and can lead to a vicious cycle (person is anxious, then notices their heart is beating fast, so they become more anxious, their heart rate increases, etc.).

The silver lining here is that in all likelihood your heart was/is fine. Anxiety has also been proposed as a risk factor for CVD but my understanding is that this is still debated. So don't go thinking your history means you'll definitely have an MI.

None of this is meant to dismiss your experience though. Not three days ago I saw a young, healthy male in the ED who thought he was having a heart attack, and (you guessed it) his EKG and labs were 100% normal. It probably happens a lot more than people realize.

By the way, I'm not saying "don't go to the doctor because that 'heart attack' is all in your head". He absolutely made the right decision by coming in (better safe than sorry).