I've signed up for Oracle Application Express for my school education purposes because I need free Oracle db hosting. I am developing a web application which I would like to be connected to the db which Oracle given me with App Express. My problem is that I don't know where to get connection string for this db or if it is even possible to get.
If I understand your question, you're trying to use the database provided at apex.oracle.com as just a standard Oracle db and build your own independent web app using that as the backend db? If so, you can't. The apex.oracle.com setup is designed purely for learning and experimenting with apex.
This is confirmed here
https://forums.oracle.com/forums/thread.jspa?threadID=905176
If I understood your question!
I'm not aware of any free Oracle hosting other than downloading free versions from Oracle and hosting on your own computer.