Docker is not a security tool. It does not increase security in any way or form from what a “regular” Linux system offers.
For example, password protection will not help. If other users can see/read your docker image, they can unpack it (even without starting it) and inspect the files.
Also, once the container is running, anyone who is allowed to use docker commands can attach to your container, spawn a bash shell inside it and wreak havoc.
If you are sure that they are not root on that computer, you can put the docker images into a directory to which only you have read permissions. That will keep them from reading your files, but you still need to make sure that they cannot become root (via sudo for example)
You can also use a crypto loopback mount and put your image there, which keeps people from accessing it when the container is not running. But again, if it’s running, there are numerous ways (at least for root, but most also work for other regular users) to access it (reading process memory, ptrace, docker run /bin/bash, etc.)