SQL Server 2008 - performing nightly full backups & transaction log shipping, but log file keeps growing
On top of the full backup, I added a transaction log backup just to see if this made a difference


This is a big no no.  By doing a manual transaction log backup, you can break the LSN of the log shipping secondary and cause the restores to fail, unless you used the copy_only option, which doesnt allow for truncation anyway.

There are only a few things that can cause a log not to truncate/clear, an active transaction, the recovery model set to full w/ no t-log backups, or a feature that is not working properly (mirroring, replication etc...)

You can check for open transactions by running DBCC OPENTRAN in the context of the said database.  Also, I know it may seem like a waste, but I would also confirm that your log backups are actually succeeding.  It could be a situation where the backup drive is out of space and the backups are failing.

Edit:
I forgot to add, when your log does truncate, you will want to shrink your log file as the number of VLFs will probably quite large and could degrade performance.  You can use dbcc shrinkfile