You acted as judge, jury, and executioner toward a snake that was potentially innocent. Besides, even if that snake had been the reason the baby bird was now gone, whose fault was it truly? Who was it that left a helpless bird by itself in a dark, wet cave? Who was it that thought putting a rock on a baby bird was a good way to keep it warm? Two animals are dead and/or missing because of your carelessness.
You probably had your reasons, but be really honest with yourself: were they very good reasons? You only have yourself to answer to, since everything that comes into contact with you goes missing or gets brutally murdered.