It sounds as if all your assignments were probably still using the old (2.2) assignment module.
I believe that is still available in a core install (and I'm quite sure it was in 2.9), but it is turned off (and therefore hidden) by default.
If you go to http://path/to/your/moodle/admin/modules.php and enable the Assignment (2.2) activity, do your assignments reappear?
If so, firstly, great you have them back, secondly, get them upgraded to the newer assignment style asap
A linked point on upgrade workflow in a high stakes environment such as this: what I do at least - in outline anyway... (doesn't help with the current situation, but maybe useful for others in the future)
1. On a test server (can be any computer so long as it has a LAMP/WAMP environment) copy your current moodle code and install it (don't worry about data at this stage, treat it as a fresh install)
2. Perform an upgrade as planned, including all your plugins to make sure everything still works as planned - this is just testing compatability of plugins in your combination, ensuring your theme works etc.
3. Clone your live site to the test server (this can be more complex and may need more than a localhost test set up if you are a large institution - but in that instance, I would also recommend this is done on as close to a mirror of your live setup as possible, server setup, php.ini etc)
4. Do the same kind of upgrade test on this clone as a test environment and make sure everything works as expected (e.g. your assignments are still there)
5. Backup your live site fully - codebase, moodledata & moodle database - allowing you the ability to rollback in the drastic case that something goes wrong despite your advance testing
6. Upgrade your live site