When I do leg presses with heavy weight I sometimes feel a burn at the bottom of my abdomen near the left pubic area. Like a sharp burn (like heat).?

Get it checked. This could indicate just a muscle strain or it could be an inguinal hernia especially if you hold your breath while pressing. A doctor can tell the difference.
Could be a tear. Iif this pain or sensation occurs only with heavy weights you might be tearing something. I recommend you decrease or stop this particular activity for at least two weeks and then slowly resume. If the pain returns at a lower weight, after resting for two weeks, you might have developed a hernia. Good luck. Okay to use over the counter anti-inflammatories, like motrin.