If an opponent captures a BF with Irelia and then charms my unit but I win the combat, will I conquer since I was the attacker?

Yes, you conquer. When your opponent charms your unit to a battlefield they control, your unit applies Contested status — making you the attacker. If you win the combat, you establish control and score a conquering point (Rule 464.1, Rule 459.2.b.1).

Key details:

• You are the attacker even though your opponent moved your unit and controls the battlefield. The unit that applied Contested determines who the attacker is (Rule 459.2.b.1; FAQ #590, #1092, #8296).
• Each player can score once per battlefield per turn — so even if the opponent already scored from that battlefield earlier this turn (by conquering with Irelia), that doesn't block you. Your scoring limit is separate (Rule 465; FAQ #5834).
• However, if you already scored that same battlefield earlier this turn (e.g. from a previous Hold or Conquer), then you cannot conquer it again — the once-per-turn limit applies to you (Rule 465).