Yes, the first one is grammatically correct and the second one is not (I think). Also, *headache. It would probably sound best as "My brother is suffering from a headache."
Thank you for your reply. But do both the sentences 'My brother suffers a headache' and 'My brother is suffering from a headache' have the same meaning? If the word 'headache' refers to a physical illness, which is a better way to say?