How do you know it's a wart? Did a doctor diagnose it? Did a doctor apply the TCA? That's not something you really want to apply yourself.
Because it is a moist area, it may take longer to heal, and you may need more than one treatment (this is why you need to see a doctor). How long it takes to heal varies - might be a week, or longer.
You have an active case of HPV, which is a very contagious virus. When you have symptoms, you should not have sex. Also, when your skin is raw and broken, you could expose yourself to other germs your partner may have. After it has healed, you should wear a condom for at least the next several months. It won't eliminate the risk of transmission, but it will significantly reduce it. You should also tell your partners that you have this. HPV clears from the body within 2 years, and you don't need to tell partners after that, but you should prior.
If you haven't seen a doctor, please do so. You could be putting TCA on something that isn't a wart.