How to capture outgoing packets?

Sure, start Wireshark, select your network card, and run the capture. If you want to exclude all packets that do not originate from your PC you can use a capture filter to only allow packets coming from your MAC or IP address, e.g. by using "ether src host aa:bb:cc:dd:ee:ff" (where aa:bb:... is your MAC address) or "src host w.x.y.z" where w.x.y.z is your IP address.

Then, to find all your requests, you can use a display filter like "http.request_method" to find all packets that contain a HTTP request, which will also show you the URL.