TwoHybrid, it could depend on where you are. In the US, for example, pronouncing 'a' with a long A and never a schwa may be a typical feature of a Deep South (e.g. Georgia) accent.Siehe auch: Aussprache a
There may be other regional accents with the same quirk, or in other places, it could just be typical of non-native speakers who weren't as well taught in school as you were. (-:
I don't think it matters whether the next word starts with a vowel sound. It does with the definite article, 'the,' which is pronounced with a long E, not a schwa, before a word that begins with a vowel sound: thee egg, thee orange, thee herbal tea (AE).
But with 'an,' the N separates the two vowel sounds, so 'an' is never pronounced with a long A (that is, never rhymes with 'mane' or 'pain').
In general, 'an' normally has a schwa, so it sounds like 'un-'. People who want to speak especially clearly might sometimes use a short A, so it sounds like the name Ann.
Does that answer your question?