I have had many asthma attacks where my oxygen level was normal anywhere from 95 to 99. I was still having an asthma attack and I was short of breath, wheezing, coughing with chest tightness.
Do you have a peak flow meter? If, not you should ask your doctor about that.
I have heard of alot of people besides you and I that are having an asthma attack without a low oxygen level.