Most new laptops come with trial antivirus that works 60 days or so, and you expect messages before that. But if "brand new" means brand new (you bought it yesterday) it's strange. What antivirus did your laptop come with, and was it the same antivirus that asked you to pay for a full license?
And that 'on facebook' is somewhat strange also. Of course, an antivirus popup can happen when you are doing anything (be it editing a picture, writing a document or visiting facebook) but it shouldn't be related to facebook.
How did you pay? Paypal, creditcard, cash? Can you still undo it?
It could be a scam.
It could be that after paying they send (or have sent) you a license code by e-mail and you should enter that into the anti-virus program to tell it you paid (how it could know otherwise?).