Hello and hope you are doing well.
The rash could be an allergic reaction to the medication. But it could also be due to the ongoing infection. Viral infections can cause rash. The vomiting could be due the infection or due to throat irritation. It may take awhile for the symptoms to settle down. However, if they worsen or if she develops additional symptoms like breathlessness or fever or worsening of the rash, please consult your doctor.
Hope this helped and do keep us posted.
Sorry for the delay in response.
I hope you took her back to the doctor.
Rashes ( hives ) can take up to 4 weeks to subside.
The vomiting may be related or she could have the flu.