I have an acute severe pain in my right lung every time I cough or sneeze.

Time to see a your medical practitioner.

Your doctor can properly diagnose and treat you.

That sucks. Maybe a doctor could help with that.

I'm guessing that you are in a country with less than easy access to care.
You need to expect that this could be pneumonia. This would be proven with an Xray and 'ralls,' raspy sounds heard by stethoscope. Then treated with antibiotics. In some countries, you can ask for antibiotics from a pharmacist.
It's serious.
That is, if it isn't just a pulled muscle from coughing.

The lungs are large. Pain in the front is usually in the bronchial tubes, not the lungs. You'd usually feel pain on the side or back with pneumonia. even way down toward the waist. You might have a cough, but might not.
For all anyone knows, your pain is from gallstones, which hurt on the right, under the ribs, either front or back or both.

It can be ANYTHING

I always go to a doctor when that happens... but them I don't have socialized medicine and can get an appointment right away.