A day after sexual intercourse realized my left labia majora was swollen like a ball.what could cause this?any home remedy?use heat pad?its been 4dys.

Cyst: Could be a bartholin's gland cyst or infection - though the latter is really painful. Could also be an area that bled. You can try sitz bathes - sitting in a tub of warm water for 15+ minutes several times a day. If it's painful get seen. If it doesn't start getting smaller get seen.

Labial swelling: If the swollen aspect of the left labium occurred spontaneously ("right after" intercourse) an ice pack will reduce swelling initially, but at "4 days" heat is better. If, on the other hand, you had some swelling prior to intercourse, the Bartholin's gland may be infected , enlarged, and this may need to be seen and drained, so see your gyn provider if the latter seems a better description.