The home oximeter or pulse-oximeter will track your heart rate too. A low pulse with good O2 may be a concern. In the hospital, you were likely sleeping in a reclined bed. This can help with breathing as it causes a better neck posture.

Just some ideas for consideration.

btw, I had a bad bout with low blood pressure and pulse after a ride back from California. I had fallen asleep in the truck with my head falling forward. I know that this position is very problematic for me. I was just learning this issue at the time. I spent the next week with BP of 70-80/40-50 with pulse rate in the 40's. I could barely get out of a chair.