Rashes On Neck, Hands, Vomiting After Eating. Due To Bed Bug Bites Or Bulimia?

dear doctor i have developed ten rashes on my neck and hands. i am not sure whether they are caused by bedbugs( this only happened last week, i have lived in my new place for two months and have never doubted that there are bedbugs here). furthermore, on both day I got rashes, I purged what I ate after meal. my question is, is it more likely to be caused by bedbugs or bulimia ( not a lie, but i only recently start to purge occasionally after meal..maybe once or twice a week for 2 months, because im anxious about my yo-yo weight )