Creating a new User Account (and deleting my old User) solved this issue for me.
***IMPORTANT NOTE: you will lose your conversations and User Home Folder files if you do not back them up or move them***
Create a new User by going to [System Preferences > Users & Groups]. You will need to have Admin privileges on your current User. Click the padlock image in the bottom left corner of the window and enter your User password to unlock it (if it is not unlocked already). Now click the [+] icon just above the padlock to add a new User. Select Administrator for the New Account privileges, and fill in fields for 'Full Name', 'Account Name' (Account Name may autofill), Password (you can use your current User password if you like), Verify, and Hint (optional). You will need to REMEMBER THESE DETAILS, as this will become your User profile.
Once you have made the new User, Log Out of your current User by clicking the top left of your screen [ > Log Out user name]. Now, Login to the new User you created, by clicking the icon for the User and entering the password you just made. Open Messages and login with your Apple ID and corresponding password. Your computer may ask you to confirm a 6-digit PIN (which will be sent to the computer or possibly the iPhone connected to the Apple ID). Once you login with your Apple ID, try sending a picture to yourself. Hopefully it works! If not, sorry, you will have to look for another fix.
Now, Log Out again [ > Log Out user name], and Login to your previous User. Back-up all files/photos/conversations/etc. that you want to keep onto another hard drive and/or make duplicates of the files, placing them into a new folder location viewable by the other User profiles on your mac [Macintosh HD > Users > Shared > new folder name]. Doing a full back-up is safer.
Log Out and Login again to the new User you have created. If you have duplicated files and moved them to the [Macintosh HD > Users > Shared > new folder name] path, check that you can access and use all the files (if you inadvertently created an Alias for the file instead of moving the actual file to this new folder, you will not be able to access it with your new User).
Optionally, once you have carefully MADE SURE that all of your files are accessible to your new User, you can choose to delete your previous User. Go to [System Preferences > Users & Groups], unlock the padlock again, enter your User password, select your previous User and click [–]. You will now be prompted select what to do with the Home Folder for your previous User Account. If you want to be extra safe, select [Save the home folder as a disk image] or [Don't change the home folder] (either will allow you to still recover the files in case you haven't backed them up). If you are 100% sure all your files/photos/conversations/etc. are accessible to your new User, you can select [Delete the home folder] and this will permanently delete the previous User and all files in their Home Folder.
Hope this helps!