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.
Would you like to try again by not killing forest animals for no reason?