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 firstname.lastname@example.org 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.