For your safety - try to get someone else to give it to them due to your allergy.

As for having something else prescribed for them / allergy testing - it is not usually required at this stage and it is not the first dose (generally) that gives an allergic reaction. You can develop an allergy (or true anaphylaxis) after many exposures to something or you can have an anaphylactoid reaction (same symptoms but without the immune system being involved) after a first exposure. Penicillin is a safe medication for most people and suited to many conditions. Talk to your doctor about alternatives if you are concerned, or more importantly question with your doctor each time antibiotics are prescribed whether they are actually needed or being given JIC. Unfortunately antibiotics are given far too frequently for viral illnesses.

I am significantly allergic to penicillin but so far neither child has shown any issues with it. Having said that, I was exposed to many, many, many courses of antibiotics for tonsillitis before the age of 4 which I believe lead to my allergy to the medication.