It depends on what you're trying to say.
If you mean to say that your line of reasoning is accurate, then it's, "My thinking is right/correct".
If you mean to say that a specific thought you have is accurate, then it's, "My thought is right/correct".
People usually don't mean the second one, so I'm assuming that you want to go with the first. And I personally prefer using 'correct' instead of 'right', but either one works.