So it happened to me too. I had my Sim take a picture of my pet before leaving the game and then it will always load on the "take a picture" screen, and after that, I'm not able to save. After closing the game, rebooting my computer, clearing all origin folders (Support suggestion) I gave up and created a different family. Everything seemed right until my teenager grew up, after that, I couldn't save, I got the message that I couldn't save while a Sim is aging up, but it over a week after the birthday.
I contacted EA support, we repaired with Origin, I loaded an older save of the game, but if I repeated the actions, I kept getting the same result. Finally, I had to completely delete the Sims 4 folder from the documents folder and create an entirely new family. I repeated the actions (took pictures of my pets, aged my Sim) and I was able to save.
I know this is not the solution one would like, mainly if you invested a lot of time in your family, but is what I got. Hope you find it helpful.
Community Manager
