If using the left shifter, which controls the front derailleur resulted in messing up your chain, either the shifter or the derailleur was already messed up, and the chain was a victim of the poor mechanical condition of your bike. It's hard to imagine a situation where a damaged chain would necessitate getting a new bike. But if the bike is cheap enough, with lousy components, and a lousy cheap frame, then having malfunctioning components might be enough reason to get a new bike. I've had a few times where a neighbor will bring some hand-me-down big-box-store bike over and ask if I can help fix it. Some of those times the answer has been, "You need a new shifter, and I don't think you're going to find this no-name thing in a bike store, so you'll probably need to either settle for this being a one-speed bike, or buy a different bike."

It's possible that your bike is in that category.