Finally fixed this tested and still working after 3 days, heres how.
I updated 3 weeks ago on iphone 4s and had this same issue and COULD NOT get it fixed.
I tried all the tips and crazy ideas people listed on here for example.
-Closing out random apps
-Deleting/updating apps
-Cleaning the headphone/ports
-Screwing around with the touch assistance
-NONE OF THESE WORKED or seem to only fix it for an hour if that.
Long story short the problem is iCloud.
Me and my Gf are on the same plan, but we use seperate iCloud accounts. As soon as I deleted my iCloud account off my phone, and signed into hers my sound worked. I don't mean a temp. fix that worked 15 mins ago so I came on here excited like mostly everyone else, only for it to fail an hour later. As soon as I changed accounts the sound worked and I have shut the phone off, charged it, used headphones, and it still works for over 3 days.
My suggestion would be delete your iCloud off your phone and log into someone elses in your family, or vice versa if your already on theirs and create one for yourself.