may be a little late for this but as a player that often plays top I think renekton won't be a bad pick against her if you play patient. You can let her use her mana on the waves and just dodge some of her skills, and if she all-ins on you just use slice and dice to dodge the tentacles and stun her. Before level 3 though I would focus on sustaining any poke she deals to you so start either dorans blade and a pot, or armor and pots(i don't personally start dorans sheild against her because most of her damage seems to come from her abilities).
As for champions that counter her I agree with the post above, anything with range and mobility will give illaoi trouble, and duelists such as irelia and fiora can be really good if you know how to play them.
An interesting matchup I found (only played 1 game of it though) is nasus vs illaoi. Nasus can stack his q really fast on the tentacles, and illaoi will push the wave if she tries to poke through your minions so just sitting back and farming nasus q can make you a beast later on, and building frozen heart and iceborn gauntlet will give you a lot of cdr and utility against her and the adc.