Sounds more like bed bugs....look at your mattress at the seams for signs of the bugs....black spots and possible red spots.....there is a way to rid your home of these and they can multiply so do make sure you clean everything well.
you might be allergic to the bites, but it also can be another thing. Do you have any other symthoms?
Are you sure it's not chicken pox? A month would be abnormally long for them, but it sounds very possible.