personally, i wonder if letters of interest really work.
i thought i wrote a pretty good letter of interest to a school after my interview. it's the only LOI I sent. many, many weeks later, they sent me an e-mail telling me that my app had received a "very favorable review" but they wanted to gauge my level of interest in the school before they made a decision. so basically, i think that sending a letter of interest (that was not a definitive letter of intent) led them to conclude that they were not my first choice (which was correct).
as others have mentioned, getting additional letters of rec. and other supporting material is probably more important than writing a letter yourself. in this age of word processors and instant access to information on the internet, letters of interest are incredibly easy to produce, and probably not worth much. you might as well write them, since everyone else is.
if your school's premed advisor has any kind of working relationship with any of the admissions offices, you can have your advisor call on your behalf to ONE of these schools.