I am assuming that you are the same Apple ID for both devices (Home and Office iPhones). You probably also have the Text Message Forwarding feature turned to ON in Settings ➔ Messages.
You can solve this immediately by using two separate Apple IDs. One for each iPhone. At that point everything will be completely separate including Contacts, Notes etc.
If you want to continue to use the same Apple ID for both devices then you will need to set Text Message Forwarding to OFF and uncheck the unwanted phone number from Send & Receive in Settings ➔ Messages. Here is how-
(1) Open Settings ➔ Messages ➔ Send & Receive ➔ UNCHECK the number that does not belong to that particular iPhone. CHECK Start all new conversations from the phone number that belongs to that iPhone. Do this on both iPhones.
(2) Open Settings ➔ Messages ➔ Text Message Forwarding ➔ Set everything to OFF. Do this on both iPhones.
(3) Turn OFF iCloud for Text Messages on both iPhones. Open Settings ➔ Apple ID (Your Name at Top) ➔ iCloud ➔ Messages - Set this to OFF.
This should take care of Messages and Images appearing on both iPhones issue. For best results delete all text messages and start fresh threads on both iPhones.
Axel F.