Thank you for the query.
Finding enlarged appendix with 19k WBC and fever and sending you home is more that risky for you and for the doctor who did this. You obviously may be suffering from appendicitis and the only way to diagnose it is to rule all other possible reasons of such conditions.
The lump in your belly button can be an umbilical hernia
(if it has gotten stuck, may be causing such symptoms as well, and should be treated right away) or persisted urachus ( this is a connection between urinary bladder
and umbilical cord
which should disappear). Persisted urachus gives umbilicus discharge and urinary tract
It is advisable for you to go again to the doctor and have abdominal ultrasound with abdominal wall view, full blood work (CRP and WBC will tell either infection is rising or not), abdominal X-ray
(stuck hernia can cause intestines obstruction), urine analysis.
Hope this will help.