I have a / We have a

Here’s a question that I can’t find the correct grammar terminology for…

At a buxiban in Taichung I recently taught health symptons such as

I have a headache/She has a headache/We have headaches. However, to me, “We have a headache” also makes sense as each person shares the same condition. Is this correct? If so, can anyone suggest the right grammar terminology for me to google this further for I haven’t been able to confirm this yet.

Mr. Blobby

we have headaches is correct because it’s talking about the individuals each having a headache, thats why its plural.

Unless you’re part of a borg collective and are one unit and can all feel each others pain.

We have headaches.

a = 1

We do not share the same (1) headache, we all have separate, unique headaches.

It ain’t correct. That don’t mean no people talk like that, though.

I think ‘We both have a headache’ is also correct though.