For context:
* I am a young adult that has only recently started to come to terms with the fact that I feel like, and am, a guy even though I was born female.
* At three years old I started to go to daycare, and I was shy to the extreme. Apparently I hardly spoke at all while being there, which surprised my mum when she heard that, because I had absolutely no problems speaking at home. I'm still quiet and reserved, also I don't feel that I am very pro-active, and I don't really express my feelings, especially not anger (in dreams, however, I often react strongly when feeling wronged - not seldom with violence).
* I like sci-fi stories about alternative universes, different timelines, time-travelling and -paradoxes, so that kind of stuff often appear in my dreams.

I have some sort of hunch about what some things in this dream is about, but having some input from somebody else's perspective would be very helpful, and there might be things that I have missed or that can be seen from other angles.
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I was in a large university building, in which I supposedly lived, there were a few dorm rooms. At first I was just hanging around, I think a few family members were there at some point, although my memories of the first portion of the dream are hazy at best. One thing I do remember is that I heard a guy, slightly younger than myself (early 20's) read something he had written out loud, from inside of his dorm room (the door was open). He had made a factual mistake and I went into his room and told him so. After that I didn't know whether or not to stay in there, he didn't ask me to leave or anything but I barely knew him so I felt there was no point in me staying, and so I went out. I laughed a little about my actions - entering someone's room just to correct them, and then immediately leaving, and how "mansplainy" it felt (although he appreciated my correction).

Later on, I was with my past self (which I, for the sake of simplicity, will refer to as "she"), aged two or three or so, based on her appearance I'd say this was before she went into daycare. I felt very protective, the same way I am in real life with my younger siblings, I was carrying her the whole time. She had some rashes on her face, nothing dramatic, but honestly it was a bit off-putting to me, although it went away after a while.
I wanted her to know that I, her future self, is a boy, because I thought that even though she might not understand it at this point, perhaps remembering that if only in the back of her head would help her realize this sooner in life than I did (I'm not sure how this worked - whether she was myself from an alternative timeline, or if she had time-travelled and making something that would alter her future would in its turn rewrite our collective history, i.e change my past). So I mentioned it, in a low voice, because there were people around and I was scared that if they heard what I was talking about they would think I was trying to indoctrinate her or something.
I then asked her if she wanted to be a boy. She said "no". Even though I don't remember actively thinking that as a kid, it surprised me, although I couldn't be sure she really understood the question (especially since, if I recall correctly, children don't really form a sense of gender identity until age 3-4 or so).

We continued walking around (or I was walking around, carrying her) around the building, but suddenly I realized she was gone. I had no idea whatsoever when and how this could have happened, I may be a bit of a scatterbrain and prone to lose things, but a child?! I panicked, and was very frustrated with myself, to say the least. This is precisely why it's better for everyone that I don't plan on having any children, I thought, but I also realized the irony of the situation: "how the hell do you lose yourself?".
I, of course, started searching for the kid. Running around the building and looking. I noticed the university was holding an election for school president or something of the sorts. A primary school teacher of mine was a candidate, she had a table advertising her party, it was focused on feminism, with the aesthetics of wealthy grown-up girl power: lots and lots of shocking pink, shiny fabric. I thought it suited her. She is, or at least was when I knew her, a very prim and proper lady with a bit of sass.
In a hallway I ran past the guy whose writing mistake I had corrected earlier, I accidentally bumped into him, and stopped and apologize. He stopped as well, then he smacked my ass. This obviously upset me, and I also felt uncomfortable realizing, in such an icky way to boot, that he saw me as a woman. I started yelling at him, and said that my daughter was missing (I felt that "daughter" would warrant less explanation than "myself as a kid"), and then I kicked him in the crotch. It didn't feel like I kicked very hard, but he fell down on the floor, crying. I walked away and kept looking for myself.

I called out to her, the unisex nickname for her name, which is now my actual name. I wasn't sure whether I had actually been called that at that age, but using its feminine form felt wrong to me. And sure enough, I heard her answer, in a singsong tone: "You ca-an't find mee". "Yes-I-can", I replied in the same manner, this call-and-response went on for a little as I was trying to locate her voice. I eventually located it to a closed door on my right, at some sort of meeting spot in the end of a corridor.
Only half-jokingly, I thought to myself that if I hadn't found her, she would get lost in the woods, and become some sort of hermit, thus rewriting my entire past and just like that I would disappear from this university and find myself in a cabin in the woods. (I didn't think anything about the time-paradox this would create, but on the other hand I got distracted right after having thought that.)
As I was approaching the door, it opened, and out came kiddy-me, along with a handful of other kids. She seemed happy. I was relieved, and considered picking her up again, but then I had the feeling she wouldn't want that, and even if I had been really worried and wanted to keep her close to me, I had to respect that. So instead I took her hand, and we walked.

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I guess the core of the dream hardly needs an interpretation at all: I lost myself and then I found myself again.
I was also trying very hard to protect myself, only to realize that it was a bit too much. Taking the child's hand instead of carrying her around, she could walk on her own while I still knew she was nearby, and it also felt as if we were a bit more on equal terms from there on.
It feels as if I was trying to give this child-version of me a better understanding and more clarity than I had, either in an alternative universe, or as an attempt to rewrite my own history. The same, in a sense, could apply to the point where I found the child: apparently having socialized with a bunch of other kids, looking happy and content, not shy and scared at all. As for asking whether kiddy-me would want to be a boy, I think it had a lot to do with the fact that it took me relatively long to realize that I am, compared to the kind of stories about this one usually hears. It has made me doubt myself and my feelings a lot before accepting them and even taking them seriously. Maybe I was disappointed by the negative answer, because I had held out hope that a "yes" would serve as some sort of definite "proof", but alas, the kid didn't deliver and I was again left to my own devices, having to answer that question myself, that is, my present self.