I main Anivia, and I've been going up against him in 5v5 matches for a while now, and most of the time I just end up angry at his ultimate (or he's too aggressive and gets himself killed). It keeps him up for what seems like an eternity in a heated match where he's bashing my face or when he's running away, while he still maintains very high AD damage. His whirlwind ability allows him to easily escape or chase due to the speed boost, especially around the jungle or when I attempt to wall him since he can simply go through them. My stun doesn't last long enough to keep him at bay for very long due to the cooldown, and my ultimate, while slowing his movement and attack speeds, just isn't enough. I buy armor, health and resists to aid my survivability, so don't assume I'm just a silly glass cannon. I've seen people say to buy an [Executioner's Calling] because the DoT will finish him off (same with playing champions such as Teemo, Brand, etc.) but that item isn't viable for me, and I don't want to change my main for a single champion.
So simply asking, what do I do? (Not limited to Anivia only, just generally speaking)