I read a new collocation cough trouble which I could not found in any dictionary.

How can I form a noun + noun collocation?


The phrase you're looking for is noun adjunct or adjectival noun. In English, we can use a noun like an adjective to modify another noun. The second noun is the thing itself - in this case, trouble. The first noun, the one that works like an adjective, tells us what kind of thing it is - in this case, cough, so it is trouble regarding a cough or trouble about a cough.

This is very common in English. For example,
apple tree - a tree, of the type "apple"
car door - a door, which belongs to a car
horse race - a race, of horses
race horse - a horse, for the purpose of racing

References on noun adjuncts:
Grammar in Use: Noun Adjuncts
Noun Adjuncts (noun + noun)
Noun as Adjective

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