If your going to add shrimp don't add medicine to the tank shrimp are very sensitive to medications. Pick up a qt tank and add a pice of LR from your cycled tank and some filter media from an established tank and treat in the qt.
I would take the filter from your main tank and put it on the qt that should allow you to put your fish in right away and start treating. Put all the fish in even if they look fine and treat for the ich. Check for ammonia and nitrite daily and do wc's as needed in the qt
Saltwater ick isn't like freshwater. The statements made about temp raising and such don't do anything on the salty side of things. You will want a copper based mad to treat in your QT tank. This will be a long process and you will need to leave your display fallow for the 8 week life cycle to ensure there still isn't any living in your sandbed.