No. Only some do and I'm not disputing your particular situation. Tachycardia is just a heart rate over 100 beats per minute. Bradycardia is a heart rate less than 60 beats per minute.
In your case you have a specific condition and you're managing that with your doctor which is the correct thing to do, but the actual term, arrhythmia is a general term which may imply a normal or abnormal heart condition (sometimes the cause is also not even heart related) which may or may not require treatment. There are many kinds of arrhythmias. Some are benign (harmless) and some are malignant (can cause harm); and some require urgent intervention while others don't. Some only require treatment if they are symptomatic (cause symptoms such as fainting spells, dizziness spells, shortness of breath, chest pain, exercise intolerance) and others always require treatment. Some can be cured definitively by burning an abnormal additional connection away in the heart while others need a pacemaker (a device which paces your heart, provides the beat to cause your heart chambers to contract) or an implantable defibrillator (a device which delivers internal electrical shocks to hearts of people who have an arrhythmia called a ventricular tachycardia or ventricular fibrillation). Some require surgery to treat the underlying condition. Some require medicine to treat them or the underlying cause. Some require avoidance of certain medicines and states. Some require observation only. Some require no treatment at all and reassurance.
All of this requires a professional assessment which may involve (some or all of), a history (doc questions you) and physical (doc examines you), a resting 12 lead ECG (these 3 provide the bulk of the information in most cases), an echocardiogram, blood tests, 24 or 48 hour ambulatory ECG (Holter), treadmill tests, tilt table tests, coronary angiograms or CT/MRI, and even electrophysiological studies aka EPS, (these can sometimes cure the problem during diagnosis).
If you want to be more specific, you can use the term tachyarrhythmia, for a fast abnormal heart rate and rhythm. But even that is general.