So if the PHP application already uses port 80 and 443 I would expect that it is not possible to start docker compose at all. Does it not display you a lot of error messages if you try to?
Best to see them directly is if you stop the setup again with:
sudo docker-compose stop
and then start the up command with the -d so just:
sudo docker-compose up
It should then directly output everything into the terminal and if there are issues you should see it. You can then stop it again with ctrl+c.
Anyway I guess you would need to free up port 443 no matter what. Here are some similar issues which partly also talk about possible solutions: