Collocations for headache - noun

bad, chronic, severe, terrible
mild, slight
dull
pounding, splitting, throbbing
blinding
migraine, tension
He developed a severe migraine headache.

experience, have, suffer from
I have a splitting headache.

develop, get
We all get headaches from time to time.

complain of
The workers had complained of headaches and nausea.

bring on, cause, give sb
Exhaust fumes made him drowsy and brought on a headache.
Red wine gives me a headache.

relieve
plead
She had left the party early, pleading a headache.

medicine (esp. AmE), pill, tablet (esp. BrE)
pain (esp. AmE)

big, huge, major, real
constant

create
These regulations have created major headaches for many businesses.

headache for
Uneven cash flow proved to be a major headache for the company.