I am diagnosed intersex (among other syndromes also XXY), and in theory can't have children, but I was lucky to be able to father one child.
I had one functioning teste, and I have a non functioning ovary, and a million other weird things going on in my body. And I have a prostate, albeit an extremely atrophied one. Intersex people come in all shapes and forms, and trying to put them in types is only a rough system, because there are many overlapping cases.
Nobody can say if you are intersex or not, until you have been tested. The most simple test for it is karyotyping, which misses a lot of in between cases, but it is a good start to find your general chromosome structure.
With most intersex people you will see clear indicators for this condition on the outside of their body, I, for example, was supposed to be a male, but always looked way more female than male, I never got any of the secondary male sex characteristics.
It is very unlikely that you have a hidden vagina instead of a prostate. i have never heard of such a case. Ovaries or even a uterus is not that uncommon.
I think you should have a medical doctor check you up, and you might be intersex, but that may manifest itself different. A prostate problem can be an ugly thing, and you want to get it taken care of as soon as possible!
See a doc and go from there!
Good luck
Linde