Oh dear. Your poor DD! They're probably living in the mattress. Or the wall.
I'd be doing a ton of hot laundry. Anything that has touched that bed should go through the laundry. And since, alas, my translation of "no one else is having a problem" is "no one else is having a problem yet," wash everyone else's bedding too.
If you can't replace the mattress, vaccuum it. Sealable covers are recommended (you need something airtight). Vacuum the entire room in any case - if you don't have a vacuum cleaner with a wand attachment, borrow one, and get back into all the corners, the tops of all baseboards, *everywhere*.
It might be worth a call to the pediatrician to see if there's a treatment they recommend for the bites, or something to keep the nasty things away.
I am so so sorry you are having to deal with this. Bedbugs are making a major resurgence in the U.S. right now, and showing up in all kinds of unexpected places.