I guess you should not use the below line
count=`cat $1 | grep -c "$2"`
Instead use the above command with slight modification
count=`grep -c "$2" $1`

I want to mention you are using cat command unneccessary(useless use of cat).The line
cat $1 | grep -c "$2"
will read file twice first by "cat" and then by command "grep" and if your file is large it will cost a time to be read twice.