Since you know her birthdate, 14 Apr 1887
you should post at the Swedish genealogy page and there are some lookups volunteers there who could probably find exactly where in Sweden she emigrated from. There is also a census of 1890 they may check for you, in Sweden. Most of that information is NOT online to search, but it is on CD's that are available, and some of these volunteers have them.

Here is where you should post the same information you posted here:

http://boards.ancestry.com/localities.scan-balt.sweden.gener...

Good Luck,
Taryn

Grant county has a historical society,

GRANT COUNTY HISTORICAL SOCIETY
Box 1002 (mailing)
115 Second Street NE
Elbow Lake, MN 56531
218-685-4864
Director: Patricia Benson
gcmnhist@runestone.net
Hours: Monday through Friday 10a.m. to 12 p.m. and 1 p.m. to 4 p.m.; (Memorial Day through September) Saturday, 10 a.m. to 12 p.m. and 1 p.m. to 4 p.m.; and by appointment
www.rootsweb.com/~mngrant/hist.htm

She also could have entered through Ellis Island. ellisisland.org is a free search, just create a log-in.