This is the 15718th most frequent Russian word.
приступ
Attack; seizure; bout.
In this sentence, 'приступ' refers to a sudden onset or fit of a symptom, cough in this case.
У него был приступ кашля.
He had a fit of coughing.
Here, 'приступили' (a derivation of 'приступ') is used to mean embarking or beginning an activity.
Строители приступили к работе.
The builders started the work.
In this context, 'приступ' describes a surge or sudden overwhelming emotion, fear in this particular case.