How long is it normal for a nettle sting be swollen?

See belown: It can stay swollen for several weeks or more depending if it was removed or left to dissolve.

Stinging Nettles.: The rash & pain from stinging nettles usually resolves within several days. Wash the skin with soap & water. Make a paste of baking soda and water (sticky consistency) and spread over the affected area. In a pinch you can spit on the affected area because saliva can neutralize the chemical irritants. In the woods – apply mud to the area. Curly dock can also be rubbed on the area.