Please tell me if there is any medicine for continiously infected ear piercing?

Have it evaluated. It is not good to have an infection for long periods of time. Have it evaluated for proper antibiotic selection.
Needs assessement. Signs of infection include: ^'ed redness, warmth, swelling. ^'ed tenderness, pus, red streaking, swollen lymph nodes or fever. Recommend keeping the piercing in place (if removed – the drainage tract will close up). Call your physician for medical evaluation. Your physician may prescribe oral antibiotics or antibiotic ointments to apply to piercing site.