Yes, there's a way to do what you want to do, but it's not as simple as some keyword that dynamically creates a new variable by some name.
Assuming your grid isn't going to ridiculously large, I would recommend you take a look at std::vector<>s. Here's a few links that should help you out:
Their main advantage over arrays is that they're expandable, and for your project they seem to fit the bill perfectly. They're class templates, so you'll need to put bool in between the <>s to make them work.