Why does handwriting change?
The brain is an interconnected whole, when we have high activity in one area of the brain other connected parts are affected.

The writting is mostly controlled by the part of the brain that controls movement (lateral and medial precentral, motor cingulate and primary motor cortices, and postcentral gyrus). Research revealed that there is a direct path between amygdala and the parts of the brain that controls movement. Subsequntly writting will be affected when the amygdala is highly active.


  Using diffusion-weighted magnetic resonance imaging and probabilistic
  tractography on a cohort of 40 participants, we provide evidence of a
  structural connection between the amygdala and motor-related areas
  (lateral and medial precentral, motor cingulate and primary motor
  cortices, and postcentral gyrus) in humans. ... a direct
  amygdala-motor pathway might provide a mechanism by which the amygdala
  can influence more complex motor behaviors.


Reference

Grèzes J., Valabrègue R., Gholipour B., Chevallier C., A direct amygdala-motor pathway for emotional displays to influence action: A diffusion tensor imaging study.