my daughter just went through a very similar thing (on her legs though). her doctor said a lot of people seem to be overreacting to mosquitoes this year!
if she'll let you put ice on it, that would to help the swelling. also a baking soda paste seems to work really well. ibuprofen for inflammation, and benadryl, for the itch (just don't use benadryl liquid and benadryl cream together or you'll overdose her -- also make sure you check with your doctor about proper dosing if you go that route -- it only gives doses for kids 6 and older, but my doc put my little one on it when she was 12 mos old!).
since my daughter's reaction to her mosquito bites were SO bad, the doctor put her on zyrtec once a day and said to keep her on it during mosquito season... could be something to check with your doctor about?