I think you've hit on one of the most common experiences of ... let's just say, "us." That is: discomfort with the words that are used in various contexts and by various people to refer to us, and a struggle to find a way to speak clearly about whatever it is that defines who is meant by "us" in a clear and graceful manner.
For example, you talk about "biological sex," but that term is quite troublesome in itself. Sex is a phenotype, not genotype, resulting from the interaction of several different genes, which may or may not be located on the X or Y chromosomes, so the question as to
which phenotype or combination of phenotypes one uses to make that distinction (or to determine that the distinction doesn't apply) is a murky one indeed!
Many biologists make the distinction with regard to the size of the gametes one might produce -- it's quite useful in ecological or developmental research, but says nothing, of course, about social interactions. Others (who have different interests in the question) support the "brain-sex" model; I tend to subscribe to that model as being useful in describing the social implications of what I sometimes call "trans identities." I tend to see it as helping to explain the diversity of gender-variant experiences (including as "gender-variant" those very gender-conforming people whose only variation is that the gender they conform to is different from the one that it was assumed they would). Many proponents of the theory, however, use it to draw sharp-line distinctions.
Then there are the labels -- "transsexual," "just a man/woman," "genderqueer," "HBS/WBT," "transgender," "FTM/MTF," "->-bleeped-<-," "trans," "she-male," "two-spirit," "hijra," "third gender," etc. -- or something entirely new. Which ones are slurs, which are culturally valid, which are overly-technical or not technical enough, which have undersirable connotations, which adequtely or inadequately describe your own experience -- those are all difficult and very often bitterly disputed questions.
Kyril and NB are right on when they talk about how cultural factors influence the experience. That applies at both large and small scales -- from the region of the world and decade or century of your birth, to the particular dynamics of your family and your personal disposition. I think that however broadly or narrowly you define "us," "we" are about as representative a sample of the human population as you can come up with, something like "type-one diabetics" or "eldest children."
I suppose that doesn't answer your question of shared experiences directly, but it's something you brought up. I think the better answer is simply to read the forums, books, other web sites and blogs, find other trans people in your area, and you'll get your answer there. I hope that you will find that we have far more diversity than conformity in our population. Rejoice in that: being "one of us" doesn't mean you can't still be yourself.
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[edit -- ah, I see -- you're not actually "one of us" -- but that's fine; what I said still pretty much applies, and you're still allowed to "be yourself."
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