Should this child be prescribed penicillin?

SO...are you suggesting here that If a person gets even minor rashes for the first time after taking penicillins, he/sshe will be listed a s penicillin allergic, despite the fact ,we agree that its not true allergic reaction? Of course I do agree that patient in future, in this case, has more chances to develop an allergic reaction, so the basis for diagnosis for the first time would be prophylactic measure rather than a true allergic patient????

It looks like a true allergy, as the three cardinal signs of a "true" allergy are rash, wheezing and/or anaphylaxis. It's true that there is cross sensitivity between penicillins and cefalosporins - I thought it was about 1 in 10? Presentation of the allergic reaction determines what action to take in switching the antibiotic: A rash without any wheezing or even anaphylactic reaction would indicate it may be safe to prescribe a cefalosporin, but observation for the first 24 hours may be wise; whereas any wheezing would rule out prescribing of any beta lactams and a macrolide or some other class should be used instead.

"Lydia rings the G.P. surgery and eventually manages to speak with a G.P.", Since we know this is a Sunday (the day after Saturday morning) I cannot think of many surgeries that would be open.

Vomitting & rash could be just further symptoms of the infection for which penicillin was prescribed?