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Hi, thanks for getting in touch. It sounds like you need a full evaluation really including blood tests looking for chronic infection and possibly a camera into your throat. I would re-approach the GP and either ask for an ENT referral with some blood tests also. You are always entitled to ask for a second opinion and your doctor will at the minimum arrange for you to see another doctor for their opinion but I think you're right that further tests ought to be carried out.
I think therefore it's important you do see a specialist particularly if your symptoms haven't gone after multiple rounds of treatment. I would seek an ENT consult and take it from there.