First off, don't worry; it's perfectly normal to freak out in the swim on your first tri. For that matter, it's perfectly normal to freak out in the swim at your second tri. I have clients and athletes who are 3-4 years into their triathlon journey, and they still sort of freak out. So don't worry; that's normal.
One of the women I taught to swim this spring just did her first race (Emporia) on Sunday. And the swim did not go quite as well as she may have hoped or planned. First off, that time trial start can be a really crappy situation for the newer swimmers because they have a poor sense of how to pace themselves. So people who should be at the back of the line seed themselves too high, and people who belong more to the middle seed themselves to the back. Bottom line, my poor friend had to pass a guy who should have seeded himself waaaaay slower than he did. So she had to pass him after less than 50 m (of a 400 m swim, mind you). Passing--even passing someone way slower than you--is hard work, and after that, she had trouble recovering her breath and regaining her rhythm. From there, she was strictly in survival mode.
My first triathlon wasn't so bad. I did a lot of backstroking and sidestroking, but overall I managed to maintain a pretty good rhythm. My second tri? Not so much. It was Pumpkinman, and it was in Lake Mead, and it was frickin' cold. I was wearing a wetsuit (borrowed, natch) for the first time. I'd never swam in a wetsuit before. I had a minor panic attack right there when the gun went off. I couldn't put my face in the water; I couldn't breathe when I did. My body absolutely rejected the notion of normal freestyle breathing. So I did the elementary backstroke for the whole swim. Longest 750 m of my life.
So it's a normal thing. But what do you do about it? How do you move past that place of panic and into a place of calm?
First off, chill out. There's absolutely nothing wrong with getting pumped for a big event, but if you're new to racing and have trouble with the swim, you'll probably be better served by listening to Sounds of Meditation than the theme song from Rocky. That initial shot of adrenaline might give you the kick start you need at a bike or run race, but in a triathlon swim, it's going to freak you out. So try to get calm and Zen instead of pumped up before the swim start. There will be time to get pumped or highly focused after you've mastered the swim start.
Second, practice. This is especially important if you're going to be doing a mass start and an open water swim. If you'll be racing with a wetsuit, practice with a wetsuit. The first time you put it on, you'll be surprised at how constricting it feels, and you don't want to be starting a race feeling constricted. Not unless you enjoy hanging on to the sides of paddle boats or kayaks, anyway. If you'll be swimming in the ocean, you damn well better practice in the ocean. Nothing's going to freak you out worse than swimming through a patch of seaweed for the first time. If you're going to be starting from a beach, practice running into the water; figure out before hand how long you want to wait until you start swimming. And if there will be a mass start (if you're swimming in a lake or ocean, there will be), practice with some friends. You know, like this:
Okay. Maybe not exactly like that.
Third, know the venue. If you can, swim there before race day. You want to know how cold the water is going to be, how far it's going to look to that first turn buoy (seeing the actual distance can be freaky, the first time), what the major landmarks are, and how the swim entry/exit looks. You'll also want to acquaint yourself with any critters who might live in the water (fish and seaweed = freaky), and be familiar with the depth at various points on the course (there's a local race where you could walk most of the swim course, if you were so inclined).
And if you do all those things and you still freak out, don't worry. It happens. Now if you're into your fifth or sixth race and you're still freaking out, you might want to try something a little more advanced. I've had athletes go for hypnotherapy; I've done guided meditation with my podcast. Those are options. When it comes right down to it, though, some people are going to feel more comfortable in water than others, and it may be something that never quite comes naturally to you. If that's the case, don't worry; you'll catch 'em up on the bike and run.