I had a chest X-ray done. The doctor said everything is normal. Would an X-ray show a blood clot or othrr lung disease?

Perhaps. X-rays show changes in structure by their ability to absorb the rays. This is why bones show up best. Soft tissue changes must be dense or extensive to be seen on an xray. If your chest xray is "normal" than any diseas present is below xray threshold. Your doc, based on your clinical situation could order a ct scan or perhaps an MRI if the results would be helpful.
Normal Chest X-ray. A normal chest x-ray rules out certain chest conditions like pneumonia, fluid in the lungs, collapsed lung, tumors, enlarged heart, etc. A plain cxr can not rule out the possibility of a blood clot in the lung (pulmonary embolus.) a ct chest angiogram is helpful to diagnose that condition.