Ok, a response which is refreshing unusual and interesting. I have some thoughts.
We think like women
And yes, I do think it "makes me a woman" because I believe a person's mind matters more than their body in determining what kind of person they are allowed to be.
You're getting confused between the stereotypes that are imposed on males and females, and 'being' male or female. Welcome to potentially understanding much of the argument made on here, where many posters feel strongly that your physical body should not dictate your personality or thoughts or actions, or how you're treated individually or as a sex category.
Though you might want to free yourself from what you've written above, which implies the other way round, where if your thoughts and feelings don't correspond with stereotypes, you 'must be' the other sex, regardless of your physical body.
We feel like women
Comments as above.
We dress like women.
From an early age I wanted to wear dresses and look attractive.
As above, the stereotypes in our current society assume that women should want to wear dresses and look attractive. And the societal messages enforce this from an early age. Women who don't want to wear dresses and don't feel/want the pressure to look attractive aren't automatically men, they're just women who don't want to wear dresses and don't feel/want the pressure to look attractive. (I don't wear dresses - that doesn't make me a man)
And vice versa, in an ideal world, wouldn't it be great if the men who want to wear dresses/look attractive could crack on without judgement (it sort of happened in the 80's but still with a lot of criticism and judgement).
I sat in a WPUK meeting last year in Oxford University, surrounded by pictures of 'esteemed' men of the university from long ago, dressed in tight leggings and thigh high boots. Clothes are of an era, they're not intimately tied to your biological sex!
We act like women
I also didn't enjoy typical boys' activities like football and games of rough and tumble .I also got bullied a lot at school, mostly because I hated the idea of violence and was unable to defend myself.I also got upset very easily which didn't help the situation.
So you were a boy who didn't like stereotypical 'boy's' sports, and you didn't like violence and got upset.
This made you a boy who didn't like stereotypical 'boy's' sports, who didn't like violence and got upset. There are many boys like this. It's a crying shame that boys like these are bullied. We need to continue the fight to break stereotypes and allow boys and men to be who they are, without bullying or judgement. Not assume they must be girls or women instead.
I ended up badly envying girls and women for what I saw as a pampered and privileged position where females are expected to be emotional and passive whereas males have to be tough and competitive.
So you were a boy who envied not being able to express part of his natural personality, and therefore resented girls. I hope you've developed the self-awareness and empathy as an adult that girls and women can be equally trapped in these expectations, when they don't want to be seen as emotional and passive, and are criticised for being tough and competitive. Rather than continue your misplaced envy and resentment?
Cutting a long story short, I buried these feelings for many years and tried to get on with being a "man". Unfortunately the deep sense of unfairness about being forced into a certain social role because of my biology contributed to significant bouts of depression. I'm not proud to say this, but I also became something of a misogynist; perceiving women as a group already enjoying a lot of privilege relative to men but nonetheless demanding even more.

Eventually I cracked the puzzle. I was envious of the female gender role because, psychologically, I'm a much better fit to it than the male role. Yes, this does involve stereotypes to some degree, but I don't think this invalidates these feelings.
It doesn't make you a woman, it makes you a man who broke out of current stereotypes of what the 'male role' might be.
Your biology wasn't 'wrong'. Society is.
But that doesn't mean that women have to include you in the category of women as a result. It means we should all fight harder to ensure that men who don't feel like they conform to the stereotypes some of society (not all) place on being 'men' are free from bullying, judgement and harassment.