One sheet is "et lagen" "Sengetøjet" is "bedclothes" i.e. the sheet, the blanket and the pillow casing. So yes I think this sentence is wrong
If I am to guess the meaning of sengetojet from this sentence it is nearby impossible.
Duo will give you the translation if you hover over the word (on pc) or click on it (in the android app).
American English would only say "I have the sheet" not "the bed sheet". If it needed to be clearer the language would be "I have the sheet for the bed under my chair." Bed sheet would be understood but viewed awkward speach.