He needs high mana costs, his Troll-Pole is a very powerful skill, and I don't mean with damage, you can use it to avoid damage from a turret and stuff like that, it needs a high cost.
And you have a problem with pushing lanes? Well, that's Fizz's weakness, his counter is champs that can push lanes because he isn't good at pushing back.
EDIT: If you are having that many problems with mana though, just try and hold back a bit in the early points of the game, don't just spam your skills all game, Fizz is bad at pushing, so don't try to push to hard. If you're laning against a pusher, ask for lots of ganks. Build an early Sheen, it's a great item for him, after that build a Rod of Ages, DO NOT rush a Lich Bane, no matter how fed you are, wait until you get some AP first. RoA will give you some nice health and mana, with some AP and lane sustain, it's an all around good item for almost all mages.
With LB and RoA late game, you shouldn't be running out of mana too often, and if you are, try and ask if you can have Blue Buff.