I believe you will have more luck first using the web developer part of firefox of equivalent. Because one request to a website as seen from the user perspective may mean a lot of network trafic on various other websites, to load images, scripts, CSS and such. So filtering only on one IP makes you missing eventually a lot of interactions.
The browser should show you all HTTP requests that are made for your website access. After which you could redo it at the network level to capture all trafic and such.
Another way: make sure to have a "quiet" computer, without any extra traffic or other browsing and so (or the minimum amount of traffic), and then capture all network packets just for the time of your HTTP request, and after that filter out what you really need. Otherwise if you filter too much beforehand you may never know that you miss something.
BTW: DNS uses UDP too! And your DNS packets go to your local recursive DNS server(s) (except if you run your own recursive DNS server on the same computer?), so this is not related in any way with the website IP or such.