Here's the best I can think of for the moment:
find . -type f \ # files only
-mtime +31 \ # exclude files less than 31 days old
-printf '%Td %p\n' | # prepend filename with day of the month of last modification
grep -v '^01' |
sed 's/^[0-9][0-9] //'
Some caveats:
- depends on GNU find
- excludes files within the last 31 days, rather than strictly excluding the current month
- looks at last modification time, rather than creation time. Most filesystems don't track creation time; if yours does, you'll need some tool other than GNU find to access it
- you can't have newlines in your filenames