It does actually sound like flea bites. I thought this before you even mentioned it.
We rescued a stray cat about 6 months ago and kept it at our place for a few days, then gave it away. We didn't know (duh!) she had fleas. My daughter was also bit mostly at night (through layers of clothes) and also had huge welts. [6 moths later, she still has scars from scratching the bites so much. Poor thing, makes me so sad.]
About 2 weeks after we got rid of the cat and figured out that we HAD fleas, we had flea busters (an eco-friendly company!) come in and they guarantee one year flea-free - even if your pets bring in new fleas. Maybe you could try them...
A good way to find out if it is indeed fleas, is to take a plain white sheet of paper, put it near where you suspect your daughter is getting bit (in this case, the floor near her bed maybe) and then stomp your hands or feet beside it a few times (fleas are attracted to this type of "vibration") then just sit there for a few minutes and watch the paper, to see if you see any little black dots jump on it (sometimes you can even hear a "click" noise when they land on the paper...
If it's not fleas, I don't really have any other advice! lol. Sorry, hope this does help though and that whatever it is can be taken care of easily. I know how terrible it is to see you little in any kind of pain - and bug bites of any kind are no fun for anyone!!
Good luck!