Ill in Oslo--will medical visit be expensive?

If you need to see a doctor just go. Getting the kind of help here that you are asking for is a waste of time.

http://travel.state.gov/content/passports/english/go/health.html

Get Help with a Medical Emergency Abroad
If you or a U.S. citizen loved one become seriously ill or injured abroad, a consular officer from the U.S. embassy or consulate can assist in locating appropriate medical services and informing your family or friends. If necessary, a consular officer can also assist in the transfer of funds from the United States. However, payment of hospital and other expenses is the patient’s responsibility. You can find local medical and emergency information at the website of the U.S. embassy or consulate near the ill or injured person. Find it online at usembassy.gov.

If you haven't quite decided that you need the doctor, you can start at the 24-hour pharmacy, across from the central train station on Jernbanetorget.