My Daughter Is 15 Years Old. She Has Had A

My daughter is 15 years old. She has had a lot of sinus drainage running down her throat. It has caused her to be sick on the stomach, throwing up, some stomach pain, and difficulty eating. I took her to a walk-in clinic and they said she may be getting a sinus infection since the drainage issue has been going on for over a week or so. They put her on the ZPac and she actually seemed worse-getting up in the mornings gagging, then throwing up, stomach pain, slight headache, still alot of drainage. This is the third day on ZPac. I took her back and they said that the ZPac was not working so they gave her Cefuroxime Axetil 250 mg that she will start tomorrow twice a day. I informed them that she is allergic to penicillin/amoxocillin. They asked if she had the reaction when she was a toddler and I said yes. They said that this was a distant cousin of the penicillin group and that she would be okay to take this? I want to know if I should give this to her since it is in the same group.