If the email adress you gave on the site is the same as the one set in the paypal account you used to buy the license, it will take a few hours for the site to "update" and award you the badge.
If the adresses are different send an email to licensehelpscirra.com with your transaction ID! (paypal "receipt").
(Do it too if you see that in 24/48 hours you still haven't got the badge).
This is assuming you made a "direct payment". If you made some "virtual cheque" it will take up to a week until Scirra receives it and awards you the badge.