If you bought it then you would have got an email with your license so if you already had avast pro installed, you shouldn't have had to reinstall it again ?
So if avast was installed already and you downloaded it again and ran that all that would happen would be it would update any files (if they were out of date). So in this case it shouldn't need to reboot as all is already established (registry etc.).
So having renewed your avast pro license all you needed to do is enter the new license number that you got in the email, right click the avast 'a' icon, select About avast!. The window that opens will have License Key... button, now copy and paste the license key you should have received into that filed. Your existing license/installation should now be renewed for a further year.
Did you get that email with the license number ?