Your new work may be considered a derivative work of the original song. A derivative work uses some or all of the original work and adds new elements. The copyright owner has the exclusive right to make derivative works. Therefore, if you made a derivative work without permission it could be considered copyright infringement.
Sometimes it is acceptable to use another’s work, which is determined by the fair use defense, but be careful that you truly have fair use before relying on the fair use defense -- in the event a lawsuit occurs against you.
If this project is important to you consider getting a license to re-make the song. Consider hiring a lawyer to assess the full facts of your specific situation.
This answer includes generalizations and there are many caveats. This answer does not form an attorney client relationship.
