Hi,
Yes, Klonopin will increase your pulse while tapering. My pulse never dropped below 90 bpm at rest while tapering, and would shoot up to 125-140 bpm, many times throughout the day, after stopping the med, it took several weeks, for my heart rate to stabilize.
Tranquillizers basically puts the body to sleep (relax), slows everything down, once the med is reduced from the system, a person's system starts to awaken.
What you are experiencing is uncomfortable, but will not harm you. As MrGreen shared, try to relax and distract yourself. Drink plenty of water.
What helped me alot during those times was working online crossword puzzles.
No you're not. As your name suggests you are thinking about things so much that you are creating more anxiety. The less you think about the less of a worry it would be to you. The more focus you put on it, the more you will notice even the slightest of things. Try and distract yourself away from the pulse and heart beat for a while. You'll be just fine.