Does my unit die if I'm attacking with a 3 might unit into a 15 might unit with 13 damage?

Yes — your 3-Might unit dies, but so does the 15-Might unit: 13 damage already marked plus your 3 puts it at 16, which is lethal against 15.

Lethal is a total of marked damage, not a per-assignment amount (CR 142.4.b), so the chump attack is enough to finish the big unit. Damage is dealt simultaneously, so its 15 Might all lands on your lone attacker and kills it in the same cleanup — a straight trade, which means both players keep nothing at that battlefield.