I'm allergic to penicillin. What are the complications if I am given this antibiotic by accident?

Depends. When one is truly allergic to penicillin, if given this could cause a reaction anywhere from hives to serious anaphylaxis. A great number of people who have a history of a reaction to penicillin, especially just a rash, may not truly be allergic or at risk. A board certified allergist can do an evaluation including allergy skin tests and an oral challenge if indicated.
See below. Symptoms can vary from a mild rash to anaphylaxis and death. Allergic reactions to medications can be more severe with each additional exposure once an allergy develops. You should not take penicillin or similar medications if you have a known allergic reaction to it.