Hello, i've got a constant very mild headache almost behind the eyes which feels like brain freeze.

Brain Freeze, too: Brain freeze from ingesting ice cold foods is common & multifactorial, as are headaches. Such pain can originate from the skin, fat, muscle, blood vessels or within the cranium from great venous sinuses, their tributaries, the dura and its arteries, the falx cerebri, & the large arteries at the base of the brain (all of which have pain fibers). Also, migraines can trigger from alcohol and foods.