Sorry to hear about your little granddaughter's problem with mosquitos. I have heard that lavender and chamomille keep bugs away. You could try putting some drops of lavender or chamomille oil in some sweet almond or jojoba oil and rub it on her, or chamomille tea cooled and swabbed all over her.
As for the blisters and swelling try putting ice over the bite. Yesterday I saw an ad in a natural health magazine for a kind of zapper to be used over an insect bite. It was made in Italy. Sorry I don't have more information, but maybe Claudia, who is Italian knows of this.
Best wishes to the little one for a fun summer.
Liza