cuppkake33,
The issue you're seeing is indeed a direct result of sharing an Apple ID with others, using iMessage & iCloud in general. It's going to be in your best interest to separate your Apple IDs and get everyone a separate one. This will only get to become more difficult as your Apple ID becomes more vital down the road.
If you do decide to separate your Apple IDs, that may be a good time to give AppleCare a call so they can walk you through it. (1-800-APL-CARE, getsupport.apple.com)
Essentially, if you're both signed into one single (shared) Apple ID in Settings > iCloud, you will want to tap "Sign Out" in red at the bottom of Settings > iCloud on the device that you want to remove from your Apple ID (and later create a separate Apple ID for). This will remove this iPhone from the Apple ID. You will want to decide after tapping "Sign Out" whether you want to keep the data on the iPhone ("Keep on iPhone"/"Delete from iPhone"). It's probably in your best interest to choose to "Keep on iPhone" that way all the contacts, calendars, reminders, etc. that are stored on this iPhone stay there because there's probably a bit of both of your guys info on each of your iPhones since you shared an Apple ID for a bit of time. Once you sign out of the shared Apple ID on the other iPhone then you will essentially be able to create a new Apple ID for this second iPhone/individual. If you wish to go through contacts, calendars, reminders, etc. on the iPhone after signing out of the shared Apple ID before you create a new Apple ID that may be beneficial. The only thing to keep in mind is you do not want to go deleting data on either of the iPhone's sharing the Apple ID UNTIL you sign out of the shared Apple ID on one of the iPhones; otherwise if you delete data on one iPhone it will also delete it on the other iPhone since you would both still be signed in with the same Apple ID. After signing out of the shared Apple ID on one iPhone, delete the other person's data off the iPhone you signed out of, then you can create a new Apple ID for this iPhone and sign into iCloud (Both of which can be done in Settings > iCloud). Once you create a new Apple ID and go to sign in with it, you will want to choose to "Merge." This will place the Contacts, Calendars, Reminders, iCloud Data currently on the iPhone into the new iCloud account you created with this newly created Apple ID. At this point your iCloud accounts will be separated and data will no longer be shared between the two iPhones.
Since iCloud stores all your data it is really the account you want to have separate for each iPhone. If you don't want to setup family sharing you can continue to stay signed into one (shared) Apple ID for iTunes in Settings > App and iTunes Stores. This will not cause issues because it's just involving purchases, whereas iCloud stores a bunch of user data and syncs changes back and forth between your device and your iCloud account.
The process itself is not all that complicated once you get into the Settings and follow the steps above. However, if you don't feel comfortable don't hesitate to contact AppleCare (1-800-APL-CARE) or schedule a call at getsupport.apple.com. They'd be glad to help you separate two iCloud Apple IDs.
Hope you find this helpful!