I was absolutely terrified of the radio and incapable of using it sensibly until I went flying with a PPL with years and years of experience. He was just so laid back on the radio. It wasn't that he was good - he made mistakes, forgot what to say, misheard things, but just didn't get bothered by any of it. So the ATCOs didn't either.
That was the beginning of my learning to relax on the radio. And once I stopped panicking, people on the other end stopped getting upset. Or if they did get annoyed, I didn't worry about it. I've even been known to retaliate if ATCOs are rude to me, and I'd never have dared do that back then. Not that I'm recommending a slanging match over the radio, you understand.
It takes time, but don't worry, like everything else in aviation, it'll come.