It does seem likely this started as a yeast infection, which you could have caught from your partner. All women have yeasts
in their vaginas some of the time, and men
can get infected
, especially if uncircumcised. Whether resitant yeast is a continuing problem, or whether it is now complicated by some sort of allergic reaction or other irritation, I cannot say. Nonspecific balanitis is not an STD, and not a condition STD specialists are expert at managing -- so I can't help there either.