Can an opponent make me discard a Miracle card before I cast it, after it is revealed?
Yes. Miracle triggers upon revealing the card when you draw it. You cannot cast the card until the triggered ability resolves and you pay the cost. Until that time, the card is in your hand and subject to the effects of discard.

702.93. Miracle
702.93a Miracle is a static ability linked to a triggered ability (see rule 603.10). &quot;Miracle [cost]&quot; means &quot;You may reveal this card from your hand as you draw it if it's the first card you've drawn this turn. When you reveal this card this way, you may cast it by paying [cost] rather than its mana cost.&quot;
702.93b If a player chooses to reveal a card using its miracle ability, he or she plays with that card revealed until that card leaves his or her hand, that ability resolves, or that ability otherwise leaves the stack.