It seems giving presentations/public speaking is quite a common fear/phobia and certainly shouldn't indicate anything is wrong with you. Even the palpitations!
It's something I share with you, and having to frequently speak publicly and give presentations can cause me similar problems. Who I'm delivering to, and the content, can make the fears worse, and my background - that my audience would seemingly know something about - only seems to make matters worse.
But I have this fear, and all I can say is that having to often face it usually helps. Not always though. If I - for reasons I still don't understand - feel particularly anxious and jittery, before getting up I'll breathe in through my nose for 4 secs, hold for 7, and breathe out through my mouth for 8, and repeat. It isn't a magic cure, but does seem to be one of the few coping mechanisms I've tried that takes the edge off it all.
It's relatively easy given the very real fear you might feel about all this that there's something wrong with you, I've often felt that way, but then it's also quite common. And some people can become pretty good at being able to hide these fears when they're up there. Maybe you're also better at doing so than you might think.
Another coping mechanism I tried that was VERY useful was to record myself using my phone doing a dummy presentation a few days before. It was really insightful. One aspect I realised, watching myself in the video, is that I take myself too seriously! I basically seen myself from a perspective I didn't normally, and noticed some aspects I could focus on a bit more. And the night before, I went to bed without the fear.
Good luck.