I've just paid. Why does Facebook say I'm still a Trial Member when I use my link?

Facebook caches the copy of your page and only refreshes it once a month. It would eventually change over time but you can force it. Go to https://developers.facebook.com/tools/debug, enter the link to your profile and click Debug. It'll show you the existing version, then click Scrape Again and it will get a new version from the website.