Sara Thompson sometimes wakes up in the middle of the night and finds her balance has left her. She stumbles to the kitchen. Or to the bathroom. She suffers spells of dizziness when she tilts her head just so, and sometimes for no reason at all.

Ms. Thompson, 32, said the symptoms began during her Peace Corps service in Africa, where she took the antimalarial drug mefloquine. In a lawsuit filed earlier this week in Washington, D.C., Ms. Thompson alleges the federal volunteer program negligently provided her the drug without...