Really? Not in AusE. All aches are countable. Pains, on the other hand, are not necessarily. "I have [a] chest pain", "I have [an] abdo pain."
"I have chronic pain." Yes
"I have chronic ache." No.
Well, maybe toothache is not only used as a non-count noun, but the thing is that, in many cases, it is. And when you'd like to say I had severe headache last night, that would be wrong, since headache is primarily countable, if ever uncountable.