If I am holding to 7, this is my turn. If I conquer the other battlefield I will score to 8 or draw.

Yes, you win the game.

You held one battlefield at the start of your turn (scoring to 7), then conquered the other battlefield in the same turn. Since you have scored both battlefields this turn — one via Hold, one via Conquer — you satisfy the requirement under Rule 466.1.b.2 to gain the winning point and win. A card draw only happens if you haven't scored every battlefield that turn, but you have.