My daughter is experiencing a heart rate of lowest 101and highest 118bpm at rest, fluctuating blood pressure and tightness of the chest as well as dizziness and faint ness upon standing , she is 16 years old, is this something to be worried about?

Sure: Teens (and others) who have "dizziness" and feel faint upon standing up from sitting, or sitting up from lying down, do need an evaluation from their doctors. The goal is to find out the cause and talk about how to avoid the symptoms. Sometimes blood tests will be done, such as checking for anemia (kids or teens may get routine blood tests every 4-5 years anyway).