Hot water will kill chlamydia. The only proven way to contract chlamydia is through unprotected sex with an infected partner. You need to speak to your girlfriend. She is not coming clean to you. It's hard, I know, to wrap your head around the fact that she was unfaithful, but it's your health and your relationship and you need to talk to her about it. Your hot tub theory is grasping at straws. She cheated and you both need to get treated, end of story.
Only you can decide if you want to stay. In my case, *I* was the cheater. I got drunk and cheated ONE time and that was all it took to contract a nasty disease. It was a shameful affair and I feel nothing but remorse over it. I still beat myself up about it. He forgave me, however, and for that, I will be eternally grateful. BUT...I CONFESSED. I told him what happened, because once I knew something was wrong with me, I knew that I could not keep it a secret however much I wanted to. If your girlfriend cares about you, she will tell you. It will be up to you at that point if you are willing to stay.