Your question is a bit vague in what you require.
If you only want to check for any differences, use cmp -s oldfile newfile. That will exit with a true status if the files are the same:
if cmp -s oldfile newfile
then echo files are the same
else echo files are different
./text_processing.sh ...
fi
If you want to check that the file size has increased, then you can use wc -c (for character count), wc -l (for line count), or stat --format=%s which directly uses the metadata about the file to give the total size in bytes.
if [ $(wc -c oldfile) -lt $(wc -c newfile) ] then echo oldfile is smaller ./text_processing.sh ... fi
if [ $(wc -c oldfile) -lt $(wc -c newfile) ]
then echo oldfile is smaller
./text_processing.sh ...
fi
$( ... ) runs the enclosed command and substitutes its output into the command line. [ ... -lt ... ] tests whether the first argument is less than the second argument.
If you specifically want to check that a line has been added, then the best strategy is probably to first sort both files, and then use comm to filter out common lines:
sort -o oldfile.sorted oldfile
sort -o newfile.sorted newfile
if [ $(comm -13 oldfile.sorted newfile.sorted | wc -l) -gt 0 ]
then echo 'line(s) only found in newfile'
./text_processing.sh ...
fi
comm -13 matches lines from both files. Normally every line is output, with an indent to indiciate whether the line only occurs in the first file, or only in the second file, or in both. With -13 the lines from only the first file and the common lines are suppressed, so only those lines occuring in the second file is output. That is piped into wc -l which counts the lines, and that is tested to be greater than 0.
Note that changed lines will be represented by one line only in the first file, and another line only in the second file.