My first post! "A" vs. "AN"

Just so you know; I am American and my english is obviously going to differ somewhat from the British version. My question regards the use of "A" and "AN". My education has taught me "A" precedes words beginning with consonant sounds such as, "a car" or "a house". "AN" precedes words beginning with vowel sounds such as, "an American" or "an incredible moment". I get so frustrated and even angry when I hear supposed educated individuals (especially politicians) making statements about "an historic occasion"! I apologize in advance for any punctuation mistakes and accept criticism with no hard-feelings. Thanks!

John