Ekko can completely avoid my Chum the Waters (R) by using his Chronobreak (R) and heal back my burst I did with my WQE/WEQ Combo getting him out of ignite range at the same time, even if I ignite him before the ult. Is Ekko just a complete counter to Fizz without counter play or is there something I should be doing? 
He is a hard counter iirc. Play a champion with hard cc.
Well, you've definitely got to make sure not to try to all-in Ekko when he has his ult. This is true for every champion, not just Fizz. You've got to get his health lower than you're probably used to. Try to E him when he uses his time winder to farm (time it so you don't get hit of course), auto him with a W, and get out by Q'ing a minion.
You should still be able to burst him if he's around 50%. But do everything to try to make him burn that ult defensively. And if he chooses instead to recall, then great you can damage his tower, or go make his bot lane miserable. You do have options.
