Are you sure the code is doing what you think it's doing? Let's indent it so that we can more easily see the logic:
if [ $err_abc -gt 0 ]; then
echo "$err_AB"
else
echo "No errors found"
if [ $err_ERR -gt 0 ]; then
echo "$err_eRR"
else
echo " \
No err files found"
exit 0
fi
fi
Your second `if` block is only executing if and only if the first block's test is falsy. If you want both tests to be run in all cases, this needs to be rewritten:
if [ $err_abc -gt 0 ]; then
echo "$err_AB"
else
echo "No errors found"
fi
if [ $err_ERR -gt 0 ]; then
echo "$err_eRR"
else
echo " \
No err files found"
exit 0
fi
Also, the `exit 0` you have in your final `if` statement's `else` clause is only executed if any only if the second test is falsy. If this is not your intent, that statement should be moved appropriately.