Hello and hope you are doing well.
The rash could be Hives. They develop in response to an allergic reaction, by the release of histamine. The allergen can be medications, food, extremes of temperature, exercise and viral infections to name a few. If she developed the outbreak even before you started the medication, the most likely cause would be a viral infection and the source of her infection could be the ear. So, therapy lies in resolving the infection and anti-histamines. You may need to consult your primary care physician who will examine her and initiate appropriate therapy.
Hope this helped and do keep us posted.
Sounds like hives ...If she was on medication last week for an earache and still has the earache plus has new spots, then it could be an allergic reaction.
You should take her in to see the doctor as soon as you can.