It is possible that you could have bed bugs or have bites that are caused by some sort of bug that you can't see. If you think you have bed bugs, you should probably get a new matress and clean your home thoroughly with disinfectant. It may also help to fog your home.
You could also have some sort of dermatitis that isn't caused by bugs but an allergy to something that you are coming into contact with, or some inner allergy (such as food) that is causing you to break out.
The only way you can find out is to talk to your doctor or a dermatologist.