Various piercings take various times to heal, and it depends on your overall health and the daily care you give it.
The piercings that heal the fastest (in my experience) are genital and tongue. My belly button piercing took the longest. For me, it was 3 months. For you, it could be more like 4.
Be patient before making any changes to the piercing at all. The instructions you received are dead on. Follow them to the letter! You'll be glad you did!