Thank you for posting your question here, I will try to answer it to the best of my abilities.
First of all you should get that coil removed, it has been there pretty long. The heart burn and shoulder pain
could be because you have developed GERD
(gastro esophageal disease
), ask your doctor to run some tests for example a manometry test, to confirm the diagnosis.
Brown discharge during periods is a normal thing, it happens because in your last period all of your endometrial lining didnt flow it, that is why it is flowing out in this period. This is what makes it brown in colour and not bright red.
If you arent having any kind of pain or itching along with the brown discharge during periods, then it is nothing to worry about.
Just see your doctor to confirm about the GERD, and dont worry it can be treated.
I hope this answered your question.