I think you need to give your doctors office a call and have a detailed chat with the nurse to help calm your anxieties. Tachycardia has a wide range and not all tachycardia is of concern. Tachycardia means any heart rate that is over 100 per minute. Tachycardia is extremely common when people are anxious. Why do you say you've always had tachycardia? Have you been diagnosed or have they just told you that your heart rate was high every time you went to the doctor's office? You say that your blood tests and heart tests have been fine - it could be that it is high only during the times they are taking it due to anxiety, and then fine again.
I remember when I went to the doc's office at a very stressful time in my life. I was sitting inactive in the chair for some time, talking about an unrelated health concern to the nurse and then the doc who checked my heart rate to find it was 108 (I had tachycardia). I am healthy and my heart was functioning normally since it is supposed to speed up(possibly becoming tachycardic) during times of mental or physical stress to supply the body with more power if it happens to be needed.
The thyroid number will not stay exactly the same, it will move around, just like any basic bloodwork numbers will, and it will also change if you are on certain medications.
I'd strongly recommend you write down a list of your questions and call your doctor's office to speak with a nurse, since they know your health history, your age, and what you should or should not be concerned about. They can give answers that are specific to your situation to help ease your mind about things.
Also I am not sure your specific fears about paxil, but it is a medication that may help you feel better (it does take several weeks before it works, however). Please be sure to mention your concerns to the nurse as well.
Good luck with the phone conversation!