I was given a new Corolla when I graduated high school in 2008 and I love it. It can do more than you think, too - I've strapped large couches and a queen mattress to it! You could add a hitch and tow a trailer if you ever needed to haul BIG stuff.
I'd look at upping your deductibles and making sure you have the $1000 cash+ in the bank at all times. If you keep the Corolla it will last for at least another 15 years. Mine will be 10 years old in August, has around 135,000 miles on it, and is still running like new. I've only had to do basic maintenance on it (Oil changes, transmission fluid, new tires, etc) and it's never broken down on me. If you can lower those insurance payments, I personally would keep it.