W.W.
doesn't sound like bug bites but an allergic reaction since they are all over. Bed bugs are typically concentrated on the feet and lower legs...
Do they go away during the day?
I'd go to my physician and get checked out when I have them. Truly - it sounds like an allergic reaction instead of bed bugs.
To verify NO BUGS?? clean ALL of your bedding - all of it - bedspread/comforter, blanket, pillows, sheets...then put your mattress in one of the allergenic zippered mattress containers - not the plastic that your mattress came in....but a real mattress cover - whole mattress cover...zippered up...
Good luck!!