Is having yellow watery discharge a sign of wound infection?

Yes: The signs of wound infection are redness, tenderness, swelling and fever. Purulent drainage almost always indicates a wound infection.

Drainage normal: Anytime you have an open wound, inflammation results. Swelling (edema) in the tissues leaks out when there is an open wound. This does not necessarily mean infection as it is a normal physiologic process as is the redness, warmth and tenderness. Knee jerk antibiotics are a bad idea as they can cause superinfcetion and allergic reactions with no benefit. Antibiotics are always the last resort.

Yes: Signs of wound infection include redness, increased pain, fever, red streaks on an extremity, a wound opening up, or drainage of fluid or pus.