Alright heres a tip for 1v1 top melee vs melee...
Watch your minions health and when they move up to last hit it start auto attacking them. This makes it so that they can't hit you back right away because they are already attacking. When doing this back off if you get too much creep aggro and step into the bush to drop aggro. Learn to abuse the bush when fighting too because if it's not warded you have the jump on them because they have to face check you. I won a lot of close fights by doing that or even flashing into the bush to buy a second for a cool down.
You probably know this but just in case there's a trick that Irelia can do to win trades a lot of the time. If you see them standing next to one of their minions that is low you can Q onto it (resetting the cool down on Q) and W + E them. This makes it so if they try to run or use a leap away you can still gap close onto them with Q. And if you get really fancy you can Q in and W+E and then Q away from them to another minion taking no damage in return.
Hope that helped a little :3