Am I trans? Questioning my gender identity

Hello everyone, I just joined this website as I've read some threads and the replies of the users seemed very kind and helpful. I am Ryan, 20, gay, Italian and I am a male (or at least that's the sex I was assigned).
Lately, I've been questioning my gender identity. I'm ok with my sexual orientation, I came to terms with it long ago, and I know that I like men, and I am attracted to masculinity.
However, I started to consider another option... I might be transgender. I've always been a very feminine boy, I even looked like a girl during puberty and my voice sounded female too. I've always been attracted to cross dressing and role play, and I have a huge passion for dresses, makeup and girly stuff. In fact I started doing drag.
I've always liked girly toys such as dolls, mini-kitchens and girly colours. Also, I've always acted like a girl, quite often it was natural, some other times I voluntarily imitated women. I have feminine gestures, and I have to be careful when I meet new people or I'm in public to how I move my hands and my hips and try to act masculine to avoid being bullied.
Till not long ago, I simply used to consider myself very flamboyant, but then I told myself that I never had a masculine attitude. Ever.
When I was in school I hated being associated to the boys, I hated being in group with them, having to play with them, having to ACT like them. Even going to the changing room was a challenge for me. It was just TOO AWKWARD for me. I used to get changed in the toilet, and sometimes I even got changed in front of the girls in their locker room (they had no problem with it because we were friends). I don't know, it was terrible for me to be compared to males. I used to tell myself and other people "I am not like them. They're dirty, they're strong, they need to show their superiority. They're so full of testosterone, it's disgusting. I don't wanna be compared to them". (I know it sounds funny and it's not meant to be offensive in any way, that's just what I used to say back in school).
When I started growing up, during puberty, I fell in love for some straight guys and I'd wish I was a girl so I could be with them. Sometimes I masturbated touching the part between the scrotum and the anus (I'm sorry I don't know what that part is called) and pretend I had a vagina. Sometimes I nearly cried, because I wanted to have a vagina. Then it kinda stopped for a while, I was happy being a male, and I just did drag on a few occasions. Then I started enjoying it a lot, and started wanted to do it more. Now I tell people that I'm a drag queen but there's more to that. I don't do shows, I don't get payed. I don't do crazy makeup. I like dressing up, putting makeup on and look like a girl, when I wash my face and remove the makeup I want to cry. When I take off my "fake boobs" I want to cry. I wanna have them.
The reason I'm confused is that, I don't really consider myself a girl. I wouldn't say "I'M A GIRL!" it's more something like "I wanna be a girl". Also, I don't have a problem with people calling me a "he" or with my penis. Or at least not when I'm alone. It only gets awkward when I'm having sex with someone. I'm a bottom, and it makes me uncomfortable when people touch my penis, I don't know if I can consider this "dysphoria".

Am I transgender? Please, don't tell me that I might be gender fluid. I'd rather fall into the "binary" gender system. Thank you very much in advance and sorry if it's so long and confused, I just don't know how to put it clearly into words. If you need any other info just let me know.