What is the correct way to express this?
- I have strong back pain.
- I have a strong back pain.
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We don't usually speak about a strong pain. It's more usual to speak about intense/extreme/chronic pain
So you can say:
I have back pain, which is a general statement. It may mean that you sometimes or frequently suffer from back pain or that you are suffering from it now.
If you want to be specific about your current pain, you might say: I am suffering from back pain.
If you were just speaking about a general condition: I suffer from back pain (in the same sense that I swim or I play football.
You can insert an adjective to describe the level of pain:
I have extreme/intense back pain. You might tell this to a pharmacist or doctor if you were looking for medication.
More idiomatic would be say:
I am looking for medication to relieve intense/chronic/extreme back pain.
We don't use the article a in these constructions. But we do use it when we talk about a pain:
I have a pain in my back.