Can photos be password-protected on the camera right after shooting?

Take the memory card out of the camera immediately and store it in a secure location, your wallet is a good option in most cases but locked boxes and armed guards are also a pretty common solution (I used to transport top secret military thingies when I was younger).

If the information is sensitive enough than take the memory card any time the camera is not in your hand (leave it on a table for a minute - take out the memory card, the camera is on a tripod and you go to the other side of the room to setup the lights - take out the memory card, you get the idea)

If your camera has internal memory (common in point and shoot, practically non-existent in DSLRs and high-end cameras) double check before starting you are recording directly to the memory card and not internal memory.

Because the way memory cards work it's possible to recover information from a memory card after it's deleted, formatted and even after new data is written to the card, physically destroy the card after the job is done (the same goes for the camera's internal memory, that's why point 2 above is important).

If you go into all this trouble you should also think about your computer and backup (no point in securing the memory card with armed guards just to upload the pictures into your unsecured home computer - or to have the picture on an unencrypted backup disk just lying around somewhere)