Hello,
That is not normal. I think you should do a walk-in to the specialist's office when you are having symptoms. They usually don't like walk-ins, but tell them you are a patient and want a quick PFT and pulse O2 reading. Then if there seems to be a problem, maybe the dr will sqeeze you in.
Another option would be to get a second opinion. Did you see a pulmo or an allergist/asmatologist? I would recommend that the try an allergist if you haven't seen one. Most pulmos are critical care hospital setting doctors (life support and on O2 patients trying to stay alive) and don't treat for quality of life (my allergist's words).
Praying that you feel better.
Oxygen saturations in lung disease are a moving target. It is not unusual to have variations like you describe. Oxygen monitors if they are not registering correctly can give false measurements as well so be careful that this is not the case. The pulse needs to directly match of your own pulse to know that accurate measurement occurs. A good pulmonary doctor can virtually always figure out through various tests why you are breathless.
Both answers were excellent and helpful. I did check my pulse and it was the same as the monitor. The last time I checked my sats, my heart rate was around 130 and my sats stayed at 100%. Still not sure what to think but both answers were beneficial.