I had oral sex for the first time with a very experienced guy and now I have a sore throat could I have gonorrhea?

Probably not . I assume it was fairly recent and gonorrhea would not show up immediately. Most likely you have traumatized your throat. You should be more in control of depth and speed and not let the guy force you or be rough. Gargle with warm salt water and avoid additional trauma and if your throat does not feel better in a few days than see a doctor. Also, you should be tested for stds on a regular basis.
Depends . The timing is crucial here. Is the sore throat immediate? Next day? Condoms? Rough or gentle oral sex? Most likely it's not gonorrhea. But it is best to be safe. Did the guy ever have gc? Did he have other std's? If so, you should be checked.