PSJ,
Move of lows or highs in themselves alone do not dictate whether we for a pivot high or low.... to put it simply, a pivot is a point on chart where the trend changes..from up to down OR from down to up.
There are a lot of charts posted on this thread by Saint, Satya and others with clearly marked pivots. Going through them once again will clear all your doubts.
Yes, as per your explanation above and then if the 1 PM bar would have moved up closing above 4300(high of day), then I think you can consider 4246 as pivot.