。
I've had a slight headache since last night.
Literal
Last-night from slight headache [subject-が] continue-[ongoing-ている].
から here marks the temporal starting point: 'from last night onward.' 続いている is the ongoing ~ている of 続く ('to continue, last'), describing the headache as still in progress. 軽い ('light, slight, mild') paired with 頭痛 is a natural collocation for non-serious discomfort. Everyday health-complaint phrasing.