Sounds like you might want to think about just having the jack module itself replaced.

This pic is showing a typical headphone jack with the plug inserted. From your description it sounds like the plug end is broken off with it just far enough below the outside rim that you can get a grip on it to remove it. However, the jack module in a S7 looks to be an enclosed, encapsulated assembly. This pic is taken from here (see step 14):
https://www.ifixit.com/Teardown/Sams...Teardown/56686 
If you take it somewhere to have it worked on or you do it yourself don't forget that any work has to take into account the waterproofing features. A remote possibility is if you know someone working in the jeweler trade -- if you drill a small hole just a few centimeters deep and exactly parallel to the shaft of that broken off plug end, and then just put a tiny drop of superglue on the end of something like a toothpick. Insert into the drilled hole, let the glue set, and carefully pull the plug directly straight out. (There should be a lot of resistance in the beginning and after that it should slide right out -- note in the first pic how that outward curved metal contact conforms to the inward curve on the plug end. That friction fit is what holds the plug end into the jack).