Doing a restore will more than likely resolve the problem. Plug the phone into iTunes, select your phone under DEVICES, and press Restore. This will restore your phone to factory settings. Now, after the restore is complete, you have two options:
1) Restore from Backup
This will let you restore all of the content you had on your phone but may also restore the other person's notes and their ability to sync notes to your phone.
2) Set Up as New iPhone
Your data will not be restored, but you can always sync content back later as long as it is in iTunes. On the positive side, this would positively remove any setting that would allow someone else's notes to appear on your phone.
You will be presented with these two options after the restore. I recommend restoring from a backup first so you won't lose your data, but if it doesn't solve the problem, proceed to restore as a new phone.