Possibly. The suspected problem is that fluorescent light flickers, although a normally functioning bulb flickers so rapidly that it’s not perceived by the human eye. Evidence is mixed on whether fluorescent lights are more likely to cause headache or other discomfort than other types of lighting.
However, any kind of light that’s either excessively bright, glaring, or dim may strain the eyes and trigger a headache. To minimize that strain, position your work station to reduce glare from windows or overhead light sources. Or use desk lamps, which can be positioned and adjusted to minimize glare and optimize brightness.