What Causes Redness And Itching In Arm Post Having Anti D Injection?

Im pregnant and 10 days ago had my Anty D injunction. Few days later I noticed that my arm (where I had injunction) is red, itchy and very warm when I touch. My GP told me that I got some skin allergy and prescribed me flucloxacillin 250 mg. it's the second day I'm taking this antibiotics (4 times) a day and nothing changed. Is it really skin allergy or my body didn't accept the injunction ? Also it's safe for my baby ??

Thanks