Anxiety can definitely make someone's BP skyrocket. Not only does anxiety raise BP (fight-or-flight sympathetic activation), but usually they're tense or moving which will skew the reading even higher. That could be the reason for the difference between the arms. If I remember right, they should be within 15 mm Hg of each other - a difference greater than that could indicate peripheral artery disease. But again, anxiety and accuracy don't go together.
Quick onset could be the meds, could be the patient calming down, or could be a placebo-like effect where just the act of taking the pills starts relaxing her (especially for benzos and if this is something she takes frequently).
You handled it perfectly.