Sorry you learned this the hard way. It is 100% your own responsibility to ensure that your travel documents are in order. This has nothing to do with either the airline or the travel agent. A $200 change fee seems pretty reasonable to me. Incidentally, if you buy a separate ticket from Milan to Rome, you don’t have a connecting flight. If you miss the first leg of this, you’ll have to buy a new ticket at the airport in Milan. Be aware that Milan has two airports, travelling between them is not always smooth sailing.