Contrary to popular belief, the thing that causes you to develop as male or female isn't actually X and Y chromosomes, it's whether you develop testicles or not. All the X and Y chromosomes do is determine whether you develop ovaries or testicles, everything from that point onward is determined by hormones. Male development is driven by the action of androgenic hormones produced in the testicles (primarily testosterone and a hormone derived from it called DHT), whereas female development is what happens if those hormones aren't there. If for whatever reason the testicles fail to develop, their hormones aren't produced, and you end up with a person who developed as female instead of male despite having XY chromosomes. That's what Swyer's syndrome is.
If you have an XXY karyotype, it usually doesn't prevent you from developing testicles, but that extra X chromosome messes up their development somehow so they don't grow to full size, and don't produce as much testosterone as would happen in a male fetus whose testicles had developed fully. There's normally still enough so that you develop a penis and look male when you're born, however the low testosterone may mean that your brain doesn't fully masculinise, and if that happens you can end up psychologically gender blended or even female identified. Caroline Cossey is a good example of a person who is, in her case, XXXY, and is transgender.
i'm not sure what's happened in your case, maybe you're XXY but it affected your testicles particularly badly so they produced very little testosterone during your prenatal development, so you came out female-looking. Maybe that's where the talk of Swyer's syndrome is coming from.
I know that some of the intersex people can get a bit touchy about intersex vs transgender, but in reality many transgender people have intersex traits, and many intersex people have nonbinary gender identities.
