Yes, "vowels followed by double consonants are short" is the general rule in English. Though there are of course people like the parents of your friend Ammie who don't get that. One of the elephants at the Omaha zoo's name is Omma, but they pronounce it to rhyme with coma or
Roma instead of rhyming it with comma, which always irritates me. :)
Unfortunately, "vowels followed by a single consonant are 'long'" is not as strict in English spelling. There seem to be many women with the name
Marisa who rhyme it with
Melissa rather than
Lisa.
Of course there's also the fact that what the general American public calls a "long vowel" is really usually a diphthong, I think, in linguistic terms.