Hello, if you suspect bed bugs then kindly look for them in your bedding as they tend to lay eggs beneath the side of mattresses, right below where the stitch line is. It would be then advisable to get appropriate measures to get rid of them first. As for your rash, it would be extremely difficult to diagnose and cure the rash without having look at it first.
Next Steps
Consult a Dermatologist in person or on private chat so a diagnosis can be made after having a look at the lesions or it's pictures.