Is it OK to use WITH INIT for my Transaction Log Backup to avoid having it grow too large?
No, do not use WITH INIT for transaction log backups to the same file. If you do that, you may as well not take them in between full/diff backups.

Typically you will backup the log to a unique file each time. Each one will have some form of a timestamp in the name and have a .trn extension rather than .bak. This is mostly for management purposes - it makes it really easy to identify when a log backup was taken, when it is safe to delete, whether it should be part of your point-in-time recovery operation, etc.