If I have been following things correctly, and I may not be, Jon and Danerys do meet and each considers the other a good match, only to find out at an inoportune time that they are half brother and sister.
I think Danerys is Jon’s aunt not sister.
I think that Danerys is Jon's Aunt.
I believe his parents are Lyanna Stark and Raegar Targarian. Danny is the daughter of the mad King Aerys, sister of Raegar.
In the GOT world I don’t think that will matter much.
The Targaryens intermarried all the time. That’s one of the reasons it was thought that they were mad.