Lilly - I managed to neglect this thread for weeks so hopefully you've come to terms with your uncomfortable new class. I can relate to what you were going through, because I've been there too. My situation may be somewhat different because I've been sessional for four years but for three of them was at 75%. I'm applying for a couple of regular positions this year, though, and hope to make it out of non-reg hell!
Anyway, with respect to the insecurity that comes from being new to a course - I have definitely been there and know exactly what you mean about not liking having the students pick up on it. My advice is to stop trying so hard... I know, it's counter intuitive and if you are a perfectionist (and let's face it, you're a PhD candidate which means that you probably are!) it's especially hard, BUT: I've found that if I am putting so much into a class that I'm stressing about it all the time, then I'm not having fun in class and I'm on edge. Being on edge just leaves you open to the class scenting blood and going for the jugular. The fatal trap that I fall into when starting a new class is the feeling that I'm underprepared and that I don't know the material. One of my colleagues (no doubt fed up of my moaning about it) said: "Remember, no matter what, you are smarter than they are". My experience is that I am sadly not even the second or third smartest person in the room in an average class. However, the advice is sound if you think about it more as that you KNOW more about the subject that you are teaching than they do. If you can get this far, you can take the last step in relaxing, which is to realise that you really don't have to be omniscient up there - you don't have to know the intimate details of the text that you've had the class read, you only need to be able to discuss the key concepts and, hopefully, bring your own perspective to it - my experience is that the more of yourself that you can bring into the room, the better. When I started lecturing the real me was wetting myself somewhere far, far removed from the classroom while "instructor-me" crashed and burned in a pyrotechnical display of chin into chest mumbling and abstracted shuffling of lecture notes that I could not read because I had tried to cram so much onto a piece of paper that the text was minute...
I had two epiphanies: the first during my first year of lecturing when I started using powerpoints - what a crutch - and the second when I weaned myself off powerpoints during my third year. Just a random thought, and possibly one completely irrelevant to you, but in addition to the above, my use of powerpoints was more as a crutch than an aide and the more I tried to use them effectively (i.e. as something to augment what I was saying rather than letting the slides say it for me) the more of a crutch it became. Throwing down the crutch and staggering on by myself, so to speak, really gave me confidence and even when I'm lecturing on material that is way out of my area of specialisation, I don't really feel very stressed about it anymore. I could go on, and on, and on (and I already have) so I'll leave it at that.
YMMV - this has served me well teaching intro and second year courses, don't know how one would fare in an upper level class...