Hi.
Thanks for your query.
Beautiful presentation of the symptoms by you.
Pain from an area between belly button and right hip, and up a tad; discomfort in inner abdomen in right side, feeling of an organ on laying down, discomfort rises on coughing and soreness in the general abdomen.
This is classical book-picture of
appendicitis unless proved otherwise.
I would advise you the following.
Tests of blood, urine and stool.
Ultrasonography of the abdomen and to be confirmed by CT scan if required.
Clinical evaluation and physical examination by a General Surgeon;
Appendectomy if confirmed with a course of an antibiotic,
metronidazole and probiotics, symptomatic and supportive as for any other problems like Domperidone if nausea and vomiting and
Paracetamol if fever or so.
Do not take laxative, it is contraindicated.