Why do 7 segment LED displays break apart when I brush my teeth?
Yes, it sounds like you are seeing artifacts of toothbrush frequency vibrating your head and therefore your eyes, and that beating against the LED refresh frequency.

This is a similar effect to eating potato chips (actually anything crunchy) while watching the LED display.  In that case the head vibrations are more random, so parts of the LED display will appear to jump around randomly.  Some segments will be displayed during a head-high part of a vibration, and others during head-low.  These will appear in different locations.

LEDs are refreshed all kinds of ways.  A lot has to do with how clever or competent the engineer was that wrote the firmware.  I've seen naive refresh algorithms that simply do each digit in order.  Those have the most apparent flicker for any one refresh rate.  Better means interleave digits, sortof like interlacing of old TV scans lines.  The whole display is still refreshed at the same rate, but the apparent flicker is at least in part related to the interlace rate.  There are fancy schemes which interleave both digits and segments, but these are often not possible with common displays where whole digits are already partially wired together.