I recently applied for a job at a public organization(which functions like a government) externally, and today one of my references who is internal to the organization highly recommended me to the hiring manager. After meeting with my potential supervisor, my reference told me that someone internal to the organization already got the job even before the job was posted on the organization's website. But the supervisor also said that she will be posting the opening for the same job sometime next week, and that I should continue checking the organization's website and I should apply for that opening.
I surfed around internet for a bit and found an article about "referral cover letter" (the cover letter that mentions that the candidate was referred to the job by an internal candidate) . Should I write this referral cover letter when I apply for the job next week? I am tempted to, because although my reference told my name to my supervisor, my name is somewhat unusual and she might not recognize my name on my resume, so if I somehow mention my reference in my cover letter the supervisor will know who I am. But then like any governmental organization the organization is strict about their hiring policy (they have to follow the rule), that everyone should apply via online only.
Should I write referral cover letter to make myself stand out, or should I not? I don't want them to have a negative impression about me. I meet all of the qualification for the job, I am positive that I am a highly qualified candidate for the job.