I'm in such pain, does that mean my labia is swollen due to infection?

Labial swelling: This is nothing to fool with and would recommend you see a doctor asap especially if you have a fever>101.5f /38.6c. This could well be a simple skin infection (cellulitis) or an ingrown hair or infected or swollen cyst. But, the pelvic area has a large area of 'dead space' and infections can spread readily up into the pelvis and cause real problems. Best to play it safe and see a doc.