I bought CC AI for small businesses and I am having trouble installing it on a 3rd computer - Do I need different licenses/users for each computer i download to?

I am logged in, but everytime I go to "desktop" or download, it just gives me the info and asks if I want to download the trial verison - even though I am already paid for. I have it on my computer (owner of the company) and one of my employee's computers under a different license, but now I would like to install it on my home computer. Any suggestions?