You do need the spirometry tests to determine wether you have asthma or not. Asthma and COPD do not really show on xray

Yes, O2 sats and Chest xray are not diagnostic for asthma, you need a stress test and pulmonary function test(s) for that diagnosis. See a pulmonologist. Asthma is a disease characterized by three things:

1) inflammation of the bronchioles
2) Constriction of the muscles surrounding the bronchi
3) Mucous secretion into the bronchi tissue

the chest x-ray would show hyperinflation of the lungs while you were having an asthma attack