Hi there!
A simplified way to differentiate these 3 rather confusing terms would probably be as follow:
带: To bring something along/ To take something with you. Another similar term is 携带 (xie2 dai4)
戴: To put on something such as face mask, sunglasses/shades, hat/cap, watch etc.
穿: To wear something such as clothes, skirt, pants, shoes etc
Examples:
带运动鞋/ 携带运动鞋: bring along your sports shoes
戴眼镜: put on glasses, 戴口罩: put on mask, 戴帽子: put on a cap,戴手表: put on a watch
穿衣服: wear clothes,穿裙子: wear skirt,穿裤子: wear pants,穿鞋子: wear shoes
Hope this helps!