This sounds like a piercing bump, possibly due to local infection or a granulomatous response. The intermittent pus and swelling suggest chronic irritation or secondary bacterial infection.
Next Steps
Continue saline compresses. You may need a short course of topical antibiotic or anti-inflammatory cream. Avoid frequent touching or jewelry changes.
Health Tips
Persistent piercing bumps may require tailored treatment based on exact type—granuloma, abscess, or keloid. For a definitive diagnosis and proper care, you can do an online consult.