OK, here's a more detailed explanation...
Contacts can usually be stored in 3 places.
1. As Google contacts. These are stored on the phone and synced to your Google account (unless sync is turned off).
2. As Phone contacts. These are stored locally on the phone only and not synced.
3. As SIM contacts.
You must have been saving contacts to #2 or #3 when you thought you were saving them to #1.
I suggest trying to find all your contacts on the phone under SIM or Phone storage. I'm not familiar with your phone but the manual or Google search should help with instructions on how to access them.
Then consolidate all contacts into your existing Google account. Make a kinda master copy. This little guide will get everything into one cleaned up, easy to maintain list accessible and maintainable from your phone or computer. And automatic backup so contacts are never lost. Phone contacts are not backed up. SIM contacts is old, outdated technology that should not be considered a viable option.
To export contacts, import them to Gmail, delete all contacts on the phone and resync a clean contacts list to the phone follow these steps:
1. Turn off sync in the phone. This is to keep it from interfering with what you're about to do by trying to sync again because it detects changes being made.
2. Export contacts on the phone to Gmail. Open the Contacts app and tap Menu. Select Import/export, then Export to storage. The contacts will be exported as a .vcf file. Do this for Google contacts, phone contacts, and SIM contacts. You will probably have to export SIM contacts as a .csv file. That's ok .csv files work fine. Make a duplicate copy of the .vcf and .csv files as a safety backup.
3. Delete all contacts on the phone. This so it can have a fresh start when you download your fresh new contacts list and contacts still on the phone don't corrupt it. Then just for good measure do: Settings > Apps > All > Google contacts > Clear cache > Clear data. When finished, there should be no contacts on the phone except your Exchange contacts.
5. Login to Gmail and import the .vcf and .csv file into Gmail contacts.
6. In Gmail contacts, click on More and select Merge duplicate contacts. Then check the list for errors and do any needed edits. When satisfied export a .vcf file copy for backup and put it in a safe place.
7. Enable contacts sync on the phone and wait for the corrected contacts list to download.
Done.