Welcome to the forum.
If you want to teach one-to-one in your own home, it's not obligatory to have a qualification of any kind. Many students would prefer that you have one but, especially if you can concentrate on conversational English, you can do it using just your own knowledge.
I think it would be difficult for you to add what you learned to your CV without some mention of how you learnt it. In what way would you give that information anyway?
Student or Learner