I/O files allocating memory and print out charcters with while loops

What this program does is allows you to enter the filename at the command prompt for the file that will be used to read information from, in additon to allowing you to enter the filename at the command prompt for a file that will write information to. THe only problem I am incountering is only reading in one line when there is 3 strings of charaters and numbers

HERE IS THE CODE
#include <stdio.h>
#include <stdlib.h>
#include <ctype.h>


int main(int argc, char *argv[])
{
FILE *input, *output;
int i=0, m=0;
char character;
char *string;

if ((input = fopen(argv[1], "r")) == NULL)
{
if (argv[1]!=NULL)
{
printf("The file \"%s\" seems to be missing, so exiting.\n", argv
[1]);
exit(EXIT_FAILURE);
}
printf("Can't open an undefined file for reading, so exiting.\n");
exit(EXIT_FAILURE);
}

if ((output = fopen(argv[2], "w")) == NULL)
{
if (argv[2]!=NULL)
{
printf("Can't define the file \"%s\" for writing, so exiting.\n",argv[2]);
exit(EXIT_FAILURE);
}
printf("Can't open an undefined file for writing, so exiting.\n");
exit(EXIT_FAILURE);
}


while((character=fgetc(input))!=EOF)
{

/* Allocate an initial memory size for string */
string = (char *)malloc(2*sizeof(char));

/* If a NULL pointer is returned, display a warning! */
if (string == NULL)
{
printf("Could not allocate memory. Aborting...\n");
exit(EXIT_FAILURE);
}

while((*(string+i)=fgetc(input))!='\n')
{

/* Re-allocate memory for string */
string = (char*)realloc(string,i*sizeof(char)+2*sizeof(char));
i++;
/* If a NULL pointer is returned, display a warning! */
if (string==NULL)
{
printf("Memory re-allocation failed! Aborting...\n");
exit(EXIT_FAILURE);
}

}
printf("%s\n",string);



/* Put the '\0' character in the last element of the "array" */
*(string+i)='\0';
i++;

/* Print the string to the output file */
fprintf(output,"%s\n",string);
printf("Size of the array: %i\n",i);

/* Free up the memory since we are done with it */
free(string);

}

/* End program */
return(0);

fclose(input);
fclose(output);
return(0);
}

WHAT I GET WHEN I COMPILE IT AND RUN IT:

TRITON:gcc hw23a.c
TRITON:a.out input.txt output.txt
i my name is Dr. Some

Size of the array: 22

Size of the array: 25

Size of the array: 33
TRITON:cat output.txt
i my name is Dr. Someon


TRITON:

WHEN I SHOULD BE GETTING IS:

triton: ~> gcc hw23.c -o hw23.o
triton: ~> hw23.o input.txt output.txt
Size of memory stored for string 1: 22
Size of memory stored for string 2: 2
Size of memory stored for string 3: 10
triton: ~> cat output.txt
Output String: My name is Dr. Some
Output String: c
Output String: asdf 35 a
triton: ~>

Please read the post for new users to learn how to put your code in tags to preserve its indentation. The post contains a number of tips, makes a nice read.

I'm using Putty as a Telnet and SSH for Win32 and Unix platforms so is basic C programming in my case