Yes, David could have suffered from low self esteem. Some of us who suffer from this malady actually have less reason than David. When God told Samuel to go anoint one of Jesse's sons as the king who would take Saul's place, Jesse, David's father, didn't even think David was worthy to make the line-up. (1 Samuel 16:8-10)
God did not choose any of Jesse's sons who passed in front of Samuel - those who made the line-up - so Samuel asked Jesse, "Are these all the sons you have?" (1 Samuel 16:11) Almost as an afterthought, Jesse said "There is still the youngest, but he is tending the sheep." (Tending sheep - a very menial job.)
Jesse still seemed to think David just couldn't be the one God would choose as king. We can be thankful that God sees us differently than man. David's father saw a shepherd boy, but God saw a king when he looked at David.
Just remember, "Man looks at the outward appearance, but the LORD looks at the heart." (1 Samuel 16:7)
If you experience low self esteem, quit focusing on how people see you and even how you see yourself and remember how God sees you. He created you in His image and He sees you as worthy.