You should immediately put her on Antibiotics like Co-amoxiclav as she has most likely already developed ear infection as evidenced by oozing of pus. Besides, you should also apply an ointment locally containing topical antibiotics and steroidal mixture like Flutibact for 4-5 days. Thanks.

Hello
Pain with pus discharge suggest infection.This infection is may be due piercing is a unsterile manner
There are various stages of healing of wound.Sometimes during the process of healing in the last phase of remodelling there is formation of excess collagen or fibrous tissue that may feel like a painless knot. However, this process of healing is very complex and susceptible to interruption or failure leading to non healing or chronic infection which may be in you daughter's case.
I would suggest you to give her Augmentin Duo Syp. 5 ml thrice a day for 7 days, apply Mupimet ointment locally for 7 days and do the regular dressing. Once the infection subsides,You can apply antiscar gel like Mederma scar gel or Kelo-cote scar gel once a day and gently massage the area for about 6 weeks.
With regards

Hi welcome to Health care magic forum. We should be very cautious about cilldrens health, at least on second day. your daughter had a septic ear, due to un hygenic process, or there might be some blood vessel or a nerve besides the piercing hole. she should use medicine to cure the infection. So i advise you to consult a surgeon for diagnosis and treatment.
Besides i advise you some diet recommendations as give her more of green leafy vegetables, pulses, sprouts, milk, egg , meat, sea foods, fruits, juices, and dry fruits to increase blood, general health , and resistance to infections. Wishing for a quick recovery and thanks for calling.