Did in America? Nicoline Larsen age 20 in 1880

Hi all, I have found out that my great great grandma, Nicoline Larsen (born in 1859/1860), traveled to Chicago in 1880 with her husband, Theodor Tomas./Thomsen/Thomasen (born 1852) and one child, Ludvig Thomsen (born 1880). They got two children in Chicago, Erling Thomsen (1884) and Emilie Elisabeth Thomsen (1886). However, they traveled back to Norway in 1886. Is it possible to find the birth papers (church papers) of Emilie and Erling? What did Theodor and Nicoline do while they lived there? Work and address of living place? I appreciate all help I can get! :) (If this is the wrong place to ask for this, where else can i look?