I'm 16 I enjoy sport but my resting heart rate is at 82. Is that high?

No. It's normal. I'll bet if you record your pulse during sleep (or have someone check it), you'll find it's quite slow (50-60 would be typical at some period during the night). 80 while awake is perfectly okay.

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Is 125mcg too high of a dose of levothyroxide when my resting heart rate is is 90 to 100? And 114 to 120 when just walking around

Possibly, see Dr. Your thyroid med dose should be based on your body's hormone levels in response to treatment. If they are in check, it may not be the med. If not checked recently or not normal levels, can contribute to fast heart rate. See your dr for evaluation and bloodwork soon. Read more...
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Tachycardia. Newly evident rapid heart rates need evaluation to exclude organic pathology which can be myriad eg thyrotoxicosis, anemia, infections, pulmonary disorder, cardiac disorder et cetera. In the absence of organic underlying pathology it frequently is a reflection of cardiopulmonary deconditioning. Please check in with a local health care provider or via the concierge at this website. Read more...