What is incumbent upon me regarding the two aforementioned Umrahs, taking into consideration the circumstances of each?

If you were not certain about the onset of menstruation during the circumambulation (tawaf), then your tawaf is valid. However, if you were certain of its onset, then the tawaf is not valid according to the majority of scholars. The Hanafis, on the other hand, consider it valid, though with the obligation of a compensatory sacrifice (badanah). If you performed 'Umrah last year and took a ritual bath and circumambulated before becoming pure, then you erred. The obligation was to wait until you saw the white discharge. We hope for you leniency in adopting the opinion of those who validate the tawaf in cases of necessity.