Is there a way to get a bigger backpack in team fortress 2

Yes, with Backpack Expanders. Provided you are a Premium member of Team Fortress 2, Backpack Expanders allow you to extend your backpack 100 units at a time, up to a maximum of 2000 items (recently expanded from 1000).

Backpack Expanders are purchased from the Mann Co. Store found in-game.