Whether you go to a mall shop or a professional piercer, a high percentage of new piercings get infected. They also take longer to heal—a few months—than the 6-8 weeks we are told.
Don’t let the piercings close. This makes them harder to clean and can seal in infections.
Replace the studs with something hypoallergenic. Often the mall piercing shops have jewelry that has a high nickel content and that can cause allergies.
Povon soap is great and recommended by professional piercers. Do not touch on or near the piercing without washing hands thoroughly first. Do not clean too frequently either—usually once/day to remove any crustiness (normal) is fine.
Do not use Neosporin. As others have mentioned, it often leads to allergies. It’s such a common allergen that many derms have gotten away from using it. Also ointment residue can make it hard to clean around the piercing. Don’t use hydrogen peroxide either. It damages skin and delays wound healing. If it’s in your house, use it for cleaning, not skin:
https://health.clevelandclinic.org/what-is-hydrogen-peroxide-good-for
Warm salt water soaks are great for healing piercings. Use distilled or boiled and cooled water. Do not over-salt. You can hold the glass under the side of your head and just let the ear soak in it.
Believe it or not, piercing studios have great, well-explained after-care instructions:
https://jinxprooftattoos.com/piercing/
See a doctor if the area remains warm to the touch or red streaks develop on the skin. Also consult a doc if you see evidence of keloid scarring.