Inventor was already installed on my PC by someone else, and when I sign in, it says that I need to buy it or start a trial, despite me having an education license. I tried hitting "get products" in the education page, but this didn't change anything. I now have a trial running, but still have yet to secure the education license.
If you bought the product yourself it will be in your account, otherwise, the admin who owns the license must assign this to your autodesk account.
If you're on the normal subscription model, logging into your Autodesk account through Inventor should be enough.
If not
Go to https://accounts.autodesk.com/
Sign in with your autodesk account
Go to products and services in the top right
Here you'll find all products linked to your account.
If Inventor is not shown then it is not assigned to you.
You can get a serial here if needed.
What version of Inventor is installed?
What version of Inventor is your student license for?
As stated you can check which entitlement you have by logging into your account.
In addition to what has already been said here, just clicking Get Product does not add the product to your account. You need to at least start the download process - once started you can cancel if you have a working installation.