Great White Sharks do NOT go up rivers, they can't survive in freshwater.
The sharks you are thinking of is Bull Sharks, they have been sighted, in the Mississippi river, 500 to 600 miles from the Gulf of Mexico and have attacked a few people.
I have also heard unconfirmed reports of Bull Sharks in the Great Lakes.....but can't find any real proof.
Alot of people, when hearing of a shark attack, automatically think of a Great White Shark because they are the biggest so it makes sense why some people would believe that the Great White would have attacked them.....it didn't. The Great White actually doesn't attack THAT many people really (nor do other sharks, shark attacks are blown out of proportion), the Bull and Lemon sharks attack more.....so do a couple of other species....can't remember them right now.