2 Year Old Baby Have Lump/inflammation On The Base Of Skull With Fever

lump/ inflammation on the base of skull, with fever on a 2 year old baby. my daughter is 1 year and 9 months. She has a lump at the right lower back side of her neck. It s quite hard. It appeared 3 days ago, and she had fever. She was prescribed with amoxicillin and paracetamol. On the first day that I gave her amoxicillin, a mild rash appeared and her fever is 39.9 degrees celsius . I suspected that it was the amoxicillin and I stopped giving it to her. But, today, the rash-like redness appeared again, so I decided to continue giving her the amoxicillin. I also gave her 2.5 ml diphenhydramine, as I suspect that she s having an allergy . What bothers me is the lump/inflammation on the lower back side of her neck at the base of the skull.