All these bed bugs can be dealt with. it is best to use a non chemical treatment to make it safe for your environment . here is one i found, food grade Diatomaceous Earth found at garden centers, follow instructions, and move beds away from the walls, sprinkle in the carpet deeply, on to base boards , ( it works like borax powder for fleas and roaches) .
They’re just redbugs or chiggers.. I get them every year. I’ve lived here in SC my whole life and I have to deal with em every year about this time (late spring/early summer). Do not scratch them ! otherwise, you’ll get a nasty spreading rash ……… use alcohol or hydrocortisone cream …….don’t scratch, I know it’s hard ! you’re daughter probably has the most sensitive skin, hence the worst reaction to the bites.
The diagnosis of a bedbug infestation should be based on the clinical history and appearance of bites. A thorough inspection of sleeping quarters by the patient, a family member, or a pest control expert may demonstrate the telltale signs of an infestation15 (i.e., specks of blood-tinged insect feces and exoskeleton casts [Figure 5]). With the aid of a magnifying glass, special attention should be given to cracks and crevices of furniture, baseboards, electrical boxes, curtains, carpet, luggage, bed frames and headboards, picture frames, wall hangings, mattress and box spring seams, peeling wall paper, clothes, and linens.37 Live bedbugs can sometimes be caught by turning on a flashlight just before dawn, when bedbugs are most active, larger in appearance, and slower to scatter because of recent feeding.40
Although most furnishings need not be discarded, in some cases this may be necessary. This is especially true of heavily infested beds, sofas and recliners where bugs and eggs often reside in hard-to-reach places. Consequently, pest control firms may recommend such items be discarded, especially when in poor condition. When infested items are discarded, bagging or wrapping them prevents dislodgement of bugs en route to the trash. 
One bed bug will usually take more than one bite. Once a bed bug inserts its mouthparts and finds a suitable blood vessel, it will begin feeding. However, finding the right blood vessel may take more than one injection into the skin. In addition, bed bugs are very sensitive to movement by the host they are feeding on. Therefore, if a sleeping person moves, a feeding bed bug will probably withdraw its mouthparts and begin its search for a blood meal on another part of the body. It’s important to remember that the number of bites a person receives is not indicative of the number of bed bugs that feed on that person.
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