Well that explains it.
He went full damage while you got some health and damage.
Remember that Fizz's e passive (I think) gives him DOT damage and bonus damage when you are below a threshold of health.
He wants a close up fight. He will win every time.
You are a mage, you win with abilities not autoattacks.
So in the future respect his damage and hit him from afar.
If he uses his troll pole to go in hit him with your visions, spawn a voiding, hit him with Q and ult immediately after to keep him in place
You should win that way.