help with simple functions

Does anyone see anything wrong with these simple functions?

Basically, the "get_field" gets a word from the file of unknown length and "add_char" will add the character to the string.

The problem lies somewhere in the "add_char" function because the memory is never realloc'd. I don't get any error messages--the word is just blank when printed. :-(

Code:

char *add_char(char *string,char character)
{
    char *tmp=realloc(string,sizeof(string)+sizeof(char));
    if(tmp!=NULL)
    {
        string=tmp;
    }
    string[sizeof(string)/sizeof(char)]=character;
    return string;
}

char *get_field(FILE *inputfile)
{
    char character;
    char *field;
    
    field=(char*)malloc(sizeof(char)*2);
    
    do
    {
        character=getc(inputfile);
        field=add_char(field,character);
    }
    while(character!='\0');
    
    field[sizeof(field)]='\0';
    
    return field;
}