Prom is short for "promenade", a borrowing from the French derived from the Latin "prominare", meaning "to drive forward". To "promenade" in the original sense was simply to go for a walk, though when it appeared in English around 1567 it especially meant to walk to and fro in public view in order to display oneself or one's finery. By the late 19th century, "promenade" was being used to mean a formal ball or gala at a school or college, and it was shortened to "prom" around the same time.
promo is short for "promotion(al)", from "promote", a 14th century borrowing from Middle English derived from the Latin "promotus", past participle of promovere, literally, "to move forward", from pro- "forward" + movere "to move".
-graph(y), from the Greek for "writing". The 'first' letter of a suffix may depend on the ending of the root word to which it is attached; ergo, while the suffix is generally -ography, it may also be -agraph, as in "paragraph", or -egraph, as in "telegraph".
promography, writings about moving forward.
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