My ear is swollen, tender, and pus is coming out around a new cartilage piercing. Please help.

Hi doctor,

I have a question regarding my ear infection. Before few weeks, I got a cartilage piercing. I used a saline solution to clean the piercing as the piecer told me to avoid using alcohol or peroxide. After going to the doctor, she told me to use Peroxide to clean it. Is it fine? Another area that hurt me a lot in my ear is the eardrum. I got sharp pain over there. After a week, it became swollen, red, tender and pus came out of it. I went again to the doctor. The doctor prescribed me to use an antibiotic topical. I used it for few days and I do not have any improvement. I went to the doctor again. After that, I used an oral antibiotic. The doctor told me that he thought that it was so swollen to the point where it had to be removed. After that, I did not have any improvement. I read many articles and do not know when these symptoms get subside. I waited for a week. Again after a week, my ear became swollen where I had a cartilage piercing. It got liquid pus and a little bit of blood coming out of it. I also started to have pain behind my ears and lymph nodes in my neck became swollen. How to resolve this problem? Do I need to continue taking oral antibiotics?