Depression isn’t just a “mood” disorder. Everything you described (headaches, digestion, hormonal effects, alertness to touch) is controlled by your nervous system and modulated or controlled by your brain.
It doesn’t make sense to separate them and try to draw an arrow of causality because they’re one in the same.
Medical science has known this for a very long time, which is why standard depression inventories include questions about things like gastrointestinal problems.
Interestingly enough, many SSRI-treated patients don’t notice their mood improvements very much because the changes are gradual over many months. Usually if you interview their family members they’ll say the change is more dramatic than the patient self-rates.