Using Subdomain for new web address

I have webspace on Hostgator, main web address of http://www.cats90210.com and of course I dont want to pay for another account for my other website http://www.thecatanalyst.com. So I set up a subdomain, which automatically created “folder” http://www.thecatanalyst.com in my root. SO that’s where I installed and programmed my WordPress site for that url in subfolder analyst. Of course the real url is cats90210.com/www.thecatanalyst.com/analyst because it’s a subdomain. Main urll http://www.thecatanalyst.com will go to the first page of the wordpress and render it fine. BUT subsequent pages get a 404 unless I leave the site url inside wordpress admin as http://cats90210.com/www.thecatanalyst.com/analyst. I tried making it http://www.thecatanalyst.com/analyst but I get 404s on the subpages when I do that. There HAS to be a way to make this work that I am missing… I even tried just installing workpress into subfolder http://www.cats90210.com/analyst instead but again I get the same issue… what am I missing??? I really dont want my subpages to have to be referenced using a url that contains my parent domain name…