I also used to be terrified of public speaking. In my new career I’ll have to do it on a regular basis, and I’m fine with that. Here’s a few tips that helped me get there:
First, stop caring about what everyone thinks. Realize that when they were up there, you were worrying about what you were going to say. They’re all doing the same thing. No one in the room, except maybe the professor, is really listening, and the professor has had people pass out on the podium before. I guarantee it.
Second, unlock your knees. I know you’re doing it, and it makes you light headed.
Third, can you get into the room where your speech class is after hours? Practice talking to an empty room. Then start bringing a friendly audience (just a couple of people). By the time you have to give a speech, you should “own” the room, feel like it’s your space and the other people are there because you let them be there. The more you practice, the easier it is to get to this feeling, until you can walk into any room and own it.
Fourth, if you get lost or tripped up, go ahead and pause, take a deep breath, and move on. Even professional speakers trip over themselves sometimes. Usually you’re speaking too fast anyway, and the breath will make you slow it down. Don’t be afraid to smile a bit, even if you’re not feeling much like smiling. The people you’re talking to will subconsciously mimic your body language and facial expression. If it’s relaxed and positive, they become relaxed and positive. Then, when you see the people in the room looking receptive, you’ll relax more too. It’s a virtuous circle. All you have to do is learn to fake it at first to get it started.
I don’t know if you have a podium or not, but try not to rely on it. I was forced to learn without one, and it helped me a lot in getting my body language under control.
Seconding the suit idea too. I always dress up when I’m presenting, it’s emotional armor for me.