How to lane as Fizz early game in mid?

So I have been playing fizz, simply because Riot gifted me a Fizz skin. Now, the problem I am having with him is his early game, which so far, seems impossible to farm. Maybe it's just the champs I've played against, I don't know. I can't do a W,Q,E burst combo, as I BARELY make it worth it damage wise, AND it consumes half of my mana in just one burst. It's just not worth it as I will also lose half health in most attempts. Here's a rundown of the first 3 champs I can remember facing.

Swain - E, Q and auto harass all day. I basically can't even get close to a minion to farm. Even if I try to kill them under turret, he can still get within range of landing an E, which does a lot of damage to the squishy fish. I'm basically at his mercy. I have roughly 11 minions to his 55 when I have to back. I can easily E out of his W, but his E's and Q's are impossible to in order to preserve mana while he has his passive sustain.

Lissandra - Auto harass, and all abilities. She can poke me down and then warp to where I am to finish me off whenever she needs too. I can't trade auto attacks with her, as I can't even get close without taking a massive amount of pain.

Zed - Shurikens for days. His autos do more damage than mine, especially with shurikens, and his W. He steals all of my minions, and I simply have to sit back out of shuriken range, meaning I lose all gold, and I miss a lot of exp. I try to kill under tower, but alas, I am STILL in shuriken range and still have to dodge, and choose my minion kills ever so wisely between turret shots.

So.... are these just horrible lopsided match ups, or does Fizz not have an early game at all? I've been starting with Dorans Ring and 2 health pots, but Im thinking he HAS to go crystalline flask. My main mid champs are Swain, Xerath, and Kassadin, champs that I normally always win mid lane with, so this is coming as a tough thing to stomach.