Yeah, they generally consider 96 to be in the "tachycardia" range. Is your resting heart rate always 96? Or just sometimes. Because lots of things can cause your heart rate to go up, including stress, caffeine, cough syrups... POTS is usually when you have a fast heart rate when you're standing for a long time, or if you stand up suddenly. 150 while exercising is fine.
Don't be afraid to talk to your primary care doctor. They can do an EKG (takes all of 5 minutes to put stickers on you and click a button) and that will tell you whether your heart is beating normally. Contrary to common belief, doctors are fine with you coming in with "silly" problems. They'd rather you be paranoid about your health then go into sudden cardiac arrest while playing a sport because you were afraid to come in.
I would see a cardiologist. I have POTS, and a fast heart rate could be a symptom. You're my age when I was diagnosed. Definitely DO NOT get freaked out about it, it definitely could be nothing. But I'd get it checked out anyways.
Those heart beats are PERFECTLY fine. Normal heartbeats range from 60-100 beats per minute; higher with exercise and lower during rest. A rate of 150 is normal. They say that a normal heartbeat is 72 beats per minute (average). Truth is that that is for a man; a women's normal heart beat is actually faster, it's 82 beats per minute. Go enjoy your life....both of you and try and stop worrying about how fast or slow, your heart beat is. Take care