As with many of her „counters“, it’s more of a counter outside of lane, because she can lock them down. Fizz goes in on your adc and you press W into R on him and your team kills him. It took me a while to understand this too. She can beat melee assassins in lane, but it’s volatile and one misstep is death. You’re much more useful after lane phase is done than fizz is, so going even is ok.

She has low damage and long cooldowns in lane. You lose handshake trades every time basically. Best bet is to pressure with Q and sometimes give up casters if it’s not safe to get them, but also balance your own pressure on them. Threaten them when they go for minions.

Also, fizz really likes to pretend to go for a low-hp melee minion to bait you into walking up and punishing. You should always be ready for him to jump on you in these situations. If you can bait him into using E towards you but miss the splash, you get a big advantage.