Have you been marked complete at that school? If so they know you are interested. I doubt they’ve even read your application. I’d wait a few months and see how it plays out.
Good Luck and relax.
This^^^^. If you did not apply ED, it's all talk at this stage. EVERYONE is very interested in EVERY school they apply to, at least until they receive their first A.
Schools know this. In fact, most adcoms on SDN say most schools treat these as lies, period, based on their experiences over the years of having candidates not follow through when things change (i.e., receiving an A later that they weren't expecting from a school they like even more, or that gave them money, etc.).
Bottom line -- these things have absolutely no value until AFTER a school has expressed some independent interest in you via an II. After that, a select few schools value groveling when deciding who gets an A, or who gets called off a WL.
If and when this becomes relevant to you, you'll learn more on the school specific threads. Right now, as
@candbgirl said, your LOI is your application and your secondary fee. Nothing to do now but wait to see whether you pass the first and by far most difficult screen and receive an II. Begging before receiving an II, beyond whatever you said in your application, is not going to help at all, but WILL make you look extraordinarily desperate and lacking in confidence. Good luck!!!