community of dyers

This question has nothing to do with hand dyeing, the subject of this forum. It does not concern dyeing at all: white sheets are not dyed, unless you count fluorescent optical brighteners as dyes.

Your problem probably comes from the permanent press treatment, or possibly from the storage of the sheets before sale (an odor may transfer from another product stored in an adjacent location); both are beyond the scope of this forum. If the odor is offensive and does not wash out, return the sheets to the retailer from which you bought them. Sheets are not supposed to smell horrible.

I believe that the permanent press treatments found on most sheets on the market are resins based on formaldehyde and/or acrylamide. Most don't smell bad after washing, but some people are sensitive to the resins. It's difficult to find untreated sheets. The only sources I know for resin-free sheets are Dharma Trading Company and the Vermont Country Store.