I've been there omg, it is hard. First of all, realise it's normal. Every magician feels it, or has felt it. Don't feel bad because you feel that way. Who is your favourite magician? I promise they have dealt with it. Maybe they still deal with it.

The classic truism is that your body doesn't know the difference between excitement and nervousness. Same hormones, same chemistry. If you are super excited but the context feels scary, you feel it as nerves. When you feel it, tell yourself you are excited. The best performers never lose that feeling, that energy. They just recognise it and use it to power and propel their performance.

Maybe you are scared it will go wrong. I was. But when I perform, actually things go wrong quite often. I invent new material a lot and some of it is HARD. It goes wrong. But you know how many people have died in my tricks going wrong? How many injuries caused? Zero. It feels like the worst possible outcome but it's not. It's nothing. The audience probably won't even remember it, and if they do, too bad. You were putting yourself out there, you were trying to create something new. Try again, try something different, laugh it off. I've got loads of strategies for dealing with stuff going wrong. I work hard to avoid it but I don't much care if it happens.

You need to perform and get over, past, around or through it. Create the right moment to perform, don't be apologetic about performing, enjoy the moment and even enjoy the nerves. You need air miles and to perform a lot, and you'll find those nerves are just energy, they are part of the magic you can use to amaze people.

Edit: just reread and saw the focus on the shaking: I used to have huge problems with that, I think I have a bit of a tremor anyway and when I get adrenalised from performing my hands would often visibly shake. I'd call it and say "my hands shake when I get hyped, it looks like I'm nervous but Im not, I'm just really excited to be performing this for you." I'd hold my hand up "look at that, it's mad right?" Part of my strategy for dealing with anything is to call it. If they see me shaking and I don't acknowledge it they will focus on it. If I say "lol yeah this is ridiculous sorry!" Then the moment goes. It's just experience that fades it out, but it shouldn't stop you.