i guess feel has meaings ranging from the pure biological to the more or less just metaphorical -
I can feel being underwater because I can feel pressure. I can feel cold because my body reacts and sends signals. I can feel heat, thirst, hunger, pain, again because of what my body does. I call my reaction feeling.
I suppose emotions like love, sadness, despair trigger physiological responses that we also call feelings but that's slightly less directly to do with the body.
Then once you get to relationships it's getting less physical more to do with emotion "To Feel like...." "to feel as if....". To feel I'm at the heart of my family. To feel accepted. To feel rejected. To feel unloved. To feel lonely. "
Finally, to feel I am now part Czeckoslovakian (as I think I announced in young foolish days....) or to feel Jewish because I'm married to one. That's now getting into metaphor, opionion, simile surely? "I feel like a criminal" is a way of saying "I'm not a criminal."
You can feel British because that's a social and legal category. it's just the name for a group.
But can you feel you are a woman? I think you can feel you have grown into a woman after experiencing a certain milestone - that's feeling you are no longer merely a girl. But that's different from feeling that you are a particular biological thing, as if you had a phantom limb.