Brief Answer:
May be infection under the skin

Detailed Answer:
Hi.
Thanks for your query, albeit very small and specific.

May I please get some more information to help you more?
Since when have you got this problem ?
Any symptoms related to intestines like bloating, loose stools / constipation, nausea, vomiting, fever ?

Please post a clear picture . photograph of the abdominal wall.

Your history of rash on left side of abdomen which is looking black and blue in area with pain is suggestive of infection under the skin.

I would advise you the following:
-Get the investigations of blood- particularly for sugar, urea, creatinine , WBC count to know the severity of infection / of urine and stool.
-Consult your Doctor to have a physical examination of the area, order investigations and to give you a prescription based antibiotic, to continue motrin.
-If there is a collection of pus underneath, you may need evacuation by surgery.

-If there is problem related to the intestines you may need further investigations.

I hope this answer helps you to get a proper diagnosis and plan for the treatment.
Please feel free to ask for more if you need to or if you feel there is a gap-of-communication.
Waiting for your feedback and pictures.

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Brief Answer:
USG / MRI

Detailed Answer:
Thanks for your feedback.
The history of sharp pain after coughing bout and feeling like you pulled something is suggestive of some muscle and / or vessel tear in the location you explained.

Please get a clinical check and you will need either a High Resolution ultrasonography (USG) as cough impulse can be tested and / or MRI of the abdominal wall to know the damage by the coughing bout.

Till them strict bed-rest, mild laxative as there is history of constipation, cough syrup if coughing is still a problem, no lifting anything or in fact no activity which tightens the abdominal wall muscles.

Further treatment will depend upon the findings on investigations ...

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