You can't do this securely without your sysadmin's help, but you can do something sorta-kinda-maybe-not-really-adequate without it.
So, let's say you create your script like so:
cat >myscript <<EOF
echo "Doing something super secret here"
EOF
...but you don't want anyone who doesn't know the password to run it, even if they're using a shared account. You can do this by encrypting it:
gpg -ac <myscript >myscript.asc
...and then embedding that plaintext into a script:
#!/usr/bin/env bash
{ gpg -d | bash -s "$@"; } <<'EOF'
-----BEGIN PGP MESSAGE-----
jA0EBwMCBogTuO9LcuZg0lsB2wqrsPU8Bw2DRzAZr+hiecYTOe//ajXfcjPI4G6c
P3anEYb0N4ng6gsOhKqOYpZU9JzVVkxeL73CD1GSpcQS46YlKWJI8FKcPckR6BE+
7vqkcPWwcS7oy4H2
=gmFu
-----END PGP MESSAGE-----
EOF
That said, other users in the shared account can still collect your password if they connect to and trace your process while it's running -- running strace on the copy of bash -s will show the text being fed into its stdin. In general, you shouldn't rely on shared accounts for anything that needs to remain confidential.
setuidbit set, or an appropriate/etc/sudoersconfiguration) allowing that script to be invoked from the shared account; only when it's on the other side of a privilege boundary is it secure against someone reading its text, tracing its execution, etc.strace -p yourpid -fto trace what your shell does when you invoke the script and enter the password to decrypt it.