Is there any way you can download Python modules in ChromeOS without accessing developer mode? I am using a student Chromebook that blocks access to developer mode.
Without accessing developer mode there is not much you're going to be able to do. Your best bet would be to sign up for something like Heroku Free Dyno service (https://www.heroku.com/) and then SSH into the box and work that way.
If you would rather have something local to work on you can pick up a Raspberry Pi 3 (http://amzn.to/2fkSjn1) and SSH into that and use it as a local development server.
None of this will bypass your schools restriction on allowing access to developer mode on your Chromebook but you will at least be able to do some development while using the machine, even if you are tunneling in to another machine