My Panasonic TV screen only shows a thin line through the middle of the screen. I can hear the sound and the line that's there changes color, etc if I change channels, to match what would be on that channel.
What causes this and is it worth fixing? Or should I just look for a new TV?

There are various circuits inside a television associated with height, width, colour, contrast, brightness, etc of the picture. More than likely the component (which could be one of many) is going to cost a few pence (cents), it's the call out charge for the techie that's going to cost.
If the television is newish or cost a lot then it may be worth repairing. Your choice... cost of a call out charge + parts versus new television with warranty

I had a TV that did this I would hit it on the side on the screen went back to normal.
But after a month or so had to but new TV there was a short in the screen.