Do the pills make the sensation go away? Are there times when it's gone on it's own or is it always there? What makes it better or worse?
I think one of the more problematic things is your waking up more tired than you were before. Does taking the clonazepam help that or make it worse?
If it is stress that is causing the chest sensation, relaxation techniques are probably your best long-term solution (since the anti-anxiety meds can make you groggy). When you feel it, try deep breathing. Feel yourself relax all over. Focus on the feeling in your chest and as you breathe, feel it fade away. If it's something you can feel, it's something you can start to take some control over. It's like biofeedback, but without the equipment. Give it a try.
Good luck. If your tiredness doesn't get better, I would still pursue a diagnosis or treatment for that.