I would not put tea tree oil in my vagina. I've done it in the past and let me tell you, I seriously regretted it, because it just burned. You have to be careful with tea tree oil, it's not gentle at all. Sometimes it can do more damage than other oils as well.
The problem with oils also is they keep your skin too wet. I know that oils like coconut oil is a wonderful antifungal, but I just never felt right putting it in my vagina.
I would seriously just get on the right diet and take oral antifungals and probiotics as well. You can succeed, you can get rid of this yeast infection. Maybe you can find a safe diluted form of tea tree oil or oil of oregano or some other oil, that will not burn.