Thank you for your query.
I appreciate your concern. However it is difficult to say what the lesions are without having a look at them. They can:
1. Bug bite
(as you presume)
3. Allergic reaction
I suggest that you consult your doctor who shall examine the bumps and guide you accordingly.
I hope I have answered your query to your satisfaction.
Wishing your daughter an early recovery.
Rajiv K Khandelwal