a couple things.
You will have to pretty much re-learn the game with a wheel, but its worth it (not so much at 270 degrees, but at 720-900 its loads different)
I see no problem in him calling you a little girl, he is joking. I saw it as him telling you to be more confident and step up and do what you need to do instead of freaking out, but that comes with more seat(play) time.
I drag race in real life, and it requires more concentration than racing go karts (raced for 5 years) ever did. The races I get psyched up for I don't breath from the moment I stage until after I see a win light at the end of the track. I'm not doing that on purpose, rather its a reaction to the nerves and the thrill. The excitement from bracket racing doesn't come from going fast, its from doing everything a little more perfect than the other guy and taking the win. When my light comes on there is a rush that is like nothing else, well...actually its the same rush that everyone else describes like that...
Anyways, where I am getting at is being nervous or caring about what other people are doing/thinking won't help you. Concentrating on what you are doing will. The moment you start focusing on the other people you will screw yourself up. When racing go karts you had to learn to look past the person in front of you even though you were inches away. If you didn't learn to ignore the person in front of you, you would just start following them. You would make the same mistakes, and be stuck behind them.
This turned into a pretty long post...
anyways, ignore other people and most of your nerves will go away. The rest is most likely from you putting too much pressure on yourself. The way I try to take care of that is acting like I don't care. Its the only way I've learned to keep my wits about me.