What should one do if she can no longer discern her purity after using medication to delay her period, and feels guilty for not being able to pray as a result?

As long as you do not observe dryness between the two bloods, you are experiencing istiḥāḍah (prolonged vaginal bleeding outside of menstruation). Consider the normal blood to be menstrual blood. If its color changes to yellowish or brownish, then rule it to be purity (ṭahārah), perform ghusl (ritual bath), pray, and perform wuḍūʾ (ablution) for every prayer after its time has begun. The minimum period of purity between two menstruations is thirteen days, and the maximum duration of menstruation is fifteen days. Purity is recognized by dryness or by the white discharge (al-qaṣṣah al-bayḍāʾ).