Is there a quick way for doctors to tell if a person is allergic to penicillin?

No, although at least one is in the works and may be reviewed soon by the US Food and Drug Administration.

Developing a quick penicillin allergy test for emergency room use is seen as long overdue, partly because many people who think they are allergic to penicillin turn out not to be. They could safely take penicillin, an old but highly effective antibiotic, instead of more expensive drugs that are more likely to trigger drug resistance.