being worn or worn by the person! grammar check

Neither are incorrect, exactly, but the meaning isn't really clear and the tenses are mixed - present tense in the first phrase and past tense in the second. There is no obvious connection between 'the person' and 'the bald man' - they could be two separate people, for all we are told - so the passage has little meaning. You should always use the active mood where at all possible. Avoid the passive mood if the meaning can be as easily expressed in the active. "... after the bald man wore the wig" is better. I presume that what you mean to say is that "the bald man was unrecognisable when he wore the wig." Both 'was worn' and 'was being worn' are correct in themselves. One describes an action completed in the past while the second describes an action which was happening at the time (in the past) to which you are referring. Compare: "The church was built in 1859" with "The church was being built in 1859, It was finished the following year."

I think both are correct

I'm weak in grammar so I'm following this discussion

I don't have that's much knowledge in English grammar lol. Hope you get answer hear.