Virginia, I never heard of the penny, but who knows...
I am mildly alergic and a long time ago my doctor told me "after removing the stinger if there is one, to make a paste out of Adolph's Meat Tenderizer and liberally spread it over the sting." The enzyme in the meat tenderizer breaks down the poison and helps reduce the amount of swelling.
I have had occasion to try this and it seems to work. I made a paste and used a large band aid to keep it over the byte.
Of course YMMV,
Keith