Try this.
docker logs -f my_app --tail=100 | grep --color=always -E '^myWord'
Note the "--color=always" argument.
Another option would be to use something like https://github.com/jlinoff/colorize. I wrote it to specifically address situations like this. For example it has the ability to specify different colors for each pattern (see the help for details).
Here is an example of how to use it for your case.
$ curl -L https://github.com/jlinoff/colorize/releases/download/v0.8.1/colorize-linux-amd64 --out colorize
$ chmod a+x colorize
$ ./colorize -h
$ docker logs -f my_app --tail=100 | ./colorize '^myWord'
$ # really make it standout.
$ docker logs -f my_app --tail=100 | ./colorize -c red+greenB+bold '^myWord'