There are different products for treating shell infection. The problem is that it's difficult to tell without better photos if there is a severe infection or not. If there is a severe infection then the turtle needs to get to a vet for treatment right away. A serious infection can break through the outer layers of the shell and cause bleeding and even, when it's quite bad, break into the body cavity and become a fatal condition.
Here's some info on treating various shell conditions:
http://www.austinsturtlepage.com/Care/medshell.htm
I've treated a shell problem on my turtle with something called Hibiclense - a antiseptic hand wash for people that's sold at places like Walgreen's. I mixed a 50%/50% solution of Hibiclense and water and rubbed it on Spot's shell with a soft toothbrush. I took care not to get any on his head or in his eyes. Then I rinsed thoroughly. Hibiclense is a soap so if it isn't rinsed thoroughly it will be irritating. Then, I dry-docked him over-night. I repeated this every other day for a week. I went through the whole process a couple of times.
Spot's shell had white patches on it - not dark - so his condition wasn't the same as your turtle's. If you're feeling very uncomfortable about it, you should make an appointment with a herp vet and get an expert opinion.