Essential oils, like tea tree, should not be used directly by itself. I hope, whatever you are planning to use, has another ingredient for a carrier. Otherwise tea tree oil is very effective. You can test it on another part of your body to see if you are allergic or if it is too strong for you.
I agree that coconut oil would be better for the skin and for the purpose. I've used coconut oil as an underarm deodorant. It is absorbed into the skin very well. I did not find it oily. It is good on the face as well. It is famous for killing fungus withing the body, such as Candida.
I also get a heat rash similar to jock itch. I use a mineral rock underarm deodorant in that area after every shower. The minerals keep the rash from even starting.