What kind of arrhythmia could i have with a hr of 68 bpm and a normal heart structure? i feel shortness of breath and fatigued.

Arrhythmia : If you have arrhythmia with that heart rate, you maybe having atrial fibrillation or frequent extra beats such as PVCs and PACs.

Hard to say: given that the overalll structure and the rate is normal... There are many things that can give fatigue that are not heart. Indeed, a weak heart would tend to have an ELEVATED rate. Lung problems, anemia (although would tend to cause an elevated heart rate), obesity, pregnancy, lack of exercise, are just a few of the more common causes.