So balanitis is on the head of your penis and foreskin. This is not balanitis.
It could still be fungal - yeast, maybe, since it's responding to canestan, but it's hard to know for sure. Tea tree oil can be very irritating for some people, especially on the genitals, so it's hard to know how much is fungal (or something else) and how much is irritation from the TTO, if any.
Does your partner have any symptoms of anything? Any itching? Burning? Anything?
I'd suggest seeing a doctor at this point. You need a diagnosis, and perhaps a prescription strength cream.
I don't think it's an STD, based on how it looks (it's not herpes, for example), and because it responded to canestan, but definitely get a doctor to look at it. You've tried everything at home, so it's time to see a doctor now.
Let us know what happens.