As others say, it sounds more like an allergy, probably to some chemical in washing liquid, softener. It could also be an allergy to a toiletry or cosmetic.
I strted to itch all over when the compaany, which made the body lotion I used, changed the formulation. Once I changed it and got the other stuff out of my system the itching disappeared.
In the unlikely event it is bed bugs, just changing the mattress is not enough because they can hide in the cracks and crevaces of furniture, curtains and caprpets. You would need to get professionals in.