Yes, it's complicated.
First distinguish between "mechanical" copies of a song you RECORD and SELL. That's the 9 cents per unit for the "compulsory" license -- the published songwriter has no choice, it's automatic if you pay the statutory rate, and you can "cover" the song.
That's different from PERFORMING a cover of a song. Then, you (or more likely, the venue you perform at) pays a performing rights organization, a PRO, for that performance.
So what's a cover, and how many lyrics can you change before your song becomes a "derivative work," requiring the music publisher's permission? There's no easy answer, but I don't think changing the pronouns in song would be enough. And making a parody of a song by using your own lyrics that comment on the song or the singer might get it's own copyright protection, not requiring the music publisher's consent. But writing entirely new lyrics that don't parody the song? That would pretty clearly be an unauthorized derivative work, meaning it's copyright infringement of the songwriter's and their music publisher's rights.
Avvo doesn't pay us for these responses, and I'm not your lawyer just because I answer this question or respond to any follow-up comments. If you want to hire me, please contact me. Otherwise, please don't expect a further response. We need an actual written agreement to form an attorney-client relationship. I'm only licensed in CA and you shouldn't rely on this answer, since each state has different laws, each situation is fact specific, and it's impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.
If you do a true "cover" of the music and words, you are entitled to a compulsory mechanical license at a rate of 9.1per unit sold. But if you change the words or the music, you are not doing a cover---you are creating a derivative work. To create a derivative work, you need to negotiate a license with the composers or their publishers. Further, they can refuse to grant you such a license if they don't like your changes. Note also that sometimes there are separate copyrights for the words and music of a song, and you might need to get separate licenses from composer of the lyrics and the composer of the music (or their publishers). The world of music license clearances can be byzantine and complex, and those of us who live in this world never ceased to be amazed at how complicated it can be. Most of the time, none of this matters, because it is hard to make money selling music. Of course, if you have a "hit" and you don't get the right licenses in advance, you have a major litigation problem.
Both Ms. Koslyn and Me. Ross are right on the money. There is no easy answer without more facts. Do a little research to get comfortable with the complexities in the business.