I have the same question. We have iPads, and I want to teach iMovie, but I don't know what to do with the video once it is created because we can't upload it to Youtube. I hope someone can help.
Have you considered using Dropbox (free 2GB to begin with) but through referrals you could get up to 18GB of free storage (if you have your parents sign up via a referral to your dropbox account you will get 500MB per sign up). Or you can pay for more storage (not ideal I know). Box may also be an option or Copy (similar to dropbox with it's referrals & more storage). You would need to rotate video files in and out I would imagine to keep under your storage limit but it may be a temporary solution that could work for you and your class.
Although it can be a bit temperamental TeacherTube still exists - it may work around your county filter access.
Another possibility could be Google Drive if you have a google account.