That trans people may wonder if they're intersex is not uncommon, but I'm sorry to disappoint you. If you have to ask, then you're almost certainly not intersex. Intersex conditions are pretty obvious. They are caused by either androgen insensitivity or a chromosomal defect. Chromosomal defects have profound health effects, not just gender identity issues and certain variations in appearance. With both partial androgen insensitivity and chromosomal disorders, you'd see things like male breasts, micropenis (we're talking like two or three inches when erect), non-descended and undersized testicles, unusual pubertal development, and often sterility.
People who may not be obviously intersex only appear "normal" if the anatomical anomalies were treated at a very early by surgery and/or hormone replacement therapy. Otherwise, they would carry their ambiguous genitalia (among other things) into adulthood, which would no doubt make them extremely self-conscious.
In other words, if you look at your junk and feel that it has hardly any similarity to other guys' junk, then you're intersex. If your junk looks like typical male junk, then we can safely say that you're not intersex. And if you are intersex, how would that help you? You'd have to deal with a host of health issues on top of your transition. Would being intersex really be easier to explain to people or for them to accept? People nowadays are used to the idea of "a woman trapped in a man's body" (an oversimplication, yes, but at least it's a simple point to communicate). Good luck explaining intersex in an easy-to-understand, non-confusing way in just one sentence. People understand "male" and "female" and "man" and "woman." Most of them can't even fathom someone having a body that's "somewhere in between" or a "combination of both." A "hermaphrodite" (please note: I am not trying to label all intersex people as hermaphrodites) would sound to them like the stuff of fairy tales and myths, which is why intersex people are known as an invisible minority.
Your "girly" mind has nothing to do with being intersex or not, since the term "intersex" is only concerned with anatomical anomalies. But it is a classic sign that you are really, truly trans