Since there is only one name for parent, I would assume that Lina or Sina was not married. The Swedish word for unmarried is ogift.
Basically you are correct with a minor correction. It turns out it was Danish and the word is very close to the Swedish and Norwegian word. Uægte (danish): Mother unmarried. Based on other information on the birth itself and what appears to have happened to the child after baptism, this makes sense so I am accepting it as the correct answer.