Can anxiety cause lightheadedness and shortness of breath even if blood oxygen, blood pressure and ecg readings are all normal?

Yes, anxiety causes hyperventilation which gives you a perfect oxygen concentration but low CO2 and respiratory alkalosis which causes lightheadedness. What you call shortness of breath during anxiety attack is, in fact, hyperventilation. Blood pressure and EKG may be slightly different from your baseline but they should not be out of normal ranges.