Second round of prednisone due to unidentified sting-toxin causing swelling in finger now moved to buckles. how long can a toxin stay in your body? could this in a poisonous caterpillar? no marks just burning and then swelling and tender?

I assume you knew that you were stung on that finger. I'm not sure that another course of prednisone is needed for such a localized reaction. In view of the burning sensation, spreading swelling& tenderness,especially if significant redness is present,I'm concerned that you have an infection brewing and need oral antibiotics. Ask your physician to reevaluate you or if you should see a hand surgeon