In the US, you can not just go get an x ray.
You need an exam.
You have been self treating this, and 2 weeks is way to long.
The most common possibility here is bronchitis, as there is no fever.
This is treated with inhalers, not antibiotics.
If pneumonia, antibiotics. The vaccination does not cover many types of pneumonia.
An exam will usually reveal what you need, and you might avoid the chest x ray.
I am a double board certified US doctor.
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