That's fine, the Hebrew means essentially "a" virgin also. The young woman is chaste, as the same word is used elsewhere in the Hebrew OT. I'm not sure what else I can add. I don't know which version(s) the Apostles used at the time, but it is true that they quoted from it very often.
Isaih uses the word 'almah, which denotes a young, chaste woman, as you say, but – trouble is – the OT uses the word betuwlah in other places of the OT, which means specifically a virgin (from which virginity, or betuwlyim is derived.
Christian Bibles do not translate 'almah as young woman but instead use the word which specifically means a virgin, which Isaiah did not use.