I have been having pain on my lower left abdominal area. It hurts even more when I cough only, but the pain do go away then come back. What the causes?

Hernia. If you have having increased pain with cough, that is a sign that the pain is worse with increased abdominal pressure. This is possible indicator for a groin hernia. You should try to look for a bulge in the left lower groin area when straining or coughing. Other possibilities could be muscle strain from excessively using abdominal muscles from something like lifting or coughing.
Chronic pain/hernia. With cough increasing your symptoms you may have hernia. Your colon, a kidney, ureter and loops of small bowel are also located in your left lower abdomen. Okay to check for lumps/bulges that come and go with your cough. Okay to get checked out by your doc. If you develop fever or vomiting, go in to your doc asap.