Your daughter has a pulse rate between 113 and 120 she is 21 and on the slender side Her doctor told her not to worry unless it got close to 200 you are concerned?

Yes, I would be concerned. Normal pulse rates generally fall between 60-80 beats per minute (bpm). Anything over 100 is considered tachycardia, a rapid heart beat. It is not healthy for your heart to beat at such high rates for any appreciable amount of time. This issue needs to be addressed, even if your daughter is not having any other symptoms. I suggest that she look for another Doctor Who will address these concerns.