Your hair looks 1c to me. It looks mostly straight with body waves. I think experimenting with different products or styling could increase its waviness. You could try plopping to increase your waves, for instance.
For proper hairtyping, your hair should be unbrushed... I'm not sure if that applies when it is wet. I find my hair dries straighter if I brush it when wet after showering. My hair is wavier when I brush my hair out before I shower, then leave it unbrushed to air dry.
Your hair turning more "coarse" after brushing sounds like frizz from waves. My hair is more silky feeling and looking before I brush it out after it dries. Once I brush it out, it will straighten out more and feel more "coarse". This also happens when I brush out braid waves. My hair feels more like how you are describing when I brush out my wet hair, so I think you should try brushing your hair before you shower and take a new photo of your hair once it is dry to compare.
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