C (gcc), score: 113 103 100 96 96 91
Thanks to @ugoren, @CalculatorFeline, and @gastropner, @l4m2, and @JS1 for their tips.
z;gg(char*s){int y[238]={z=0};while(*s)z+=*y-=-y[*s++];z-y[*s++];*y/=~0;=1;}
Initializes an array of zeros, then uses the ASCII values of the characters in the string as indices to that array to keep track of the number of instances of each character in the string.