2006 Chevy Cobalt wont start, battery seems fine?

I just bought a 2006 chevy cobalt SS (NA) and got it safety and etested. ran fine up until about a few days ago. It wont start now. Battery seems perfectly fine, lights come on, alarm sounds with a nice chirp and all. It wont start with a jump from my focus and a message comes up that says check charging system. I ran my code reader and code error C0561 comes up. I delete it and it comes back. I was thinking of buying an alternator and trying to replace that. I wanted your thoughts as I am running a slim budget and after a few surprises for the safety don't want to buy an alternator if it is something else.