If these bumps have been coming and going for a while, you should go see your primary care doctor
for advice. They can take a look at the spots on your skin and help you determine what is most likely to be going on.
An allergy or sensitivity to a chemical exposure, such as a laundry detergent, can provoke something called contact dermatitis in the skin. The rash of contact dermatitis tends to be red and itching and it tends to cover large areas of skin that have come into contact with the offending agent. On the other hand, bed bugs or other insect bites tend to be smaller bumps that are not as much a generalized rash. They also tend to be clustered in areas where the bugs prefer to bite, such as the ankles or the waistline.
Therefore, based on your description, I think that bed bugs are more likely than an allergic or contact reaction. However, this suspicion would need to be confirmed by your primary care doctor. Based on what they see, they can prescribe an appropriate treatment to reduce the redness and itching.
I hope you are feeling better soon!