Is there a limit to the number of subdirectories I can create?

Yes, for ext4 systems every file or directory uses an inode, of which a limited amount are pre-allocated when the disk is first formatted. You can see what percentage of this is used by running this command:

df -hi

Look at the IUse% column. For most situations this never be exhausted, but it's possible this can lead to problems if you start out on a small disk (and therefor not many inodes) and later resize to a larger disk since inodes are not re-allocated when growing a partition. In those cases you would want to copy the file system from a small disk to a larger disk in a special way.