I was exactly the same before taking my first calls in EVERY phone job I've had.
I've just moved to a non phone role after nearly 3 years taking calls. In my role, our first few calls were with a coach plugged in so they could hear, and help when you had the caller on hold.
Hold is your friend. There's nothing wrong with saying you need to check some info before passing it on - others have given some great examples here. With complex cases or frustrated callers, I also used to say, "I can see that a lot has happened previously, would it be OK for me to pop you on hold so I can read through the notes and get an understanding of what the next step needs to be, to get this resolved?".
It was very rare that someone would argue with that, as they wanted the situation sorting, and a lot of the time they'd been passed through multiple departments, so were happy I was at least willing to try and understand.
Another good one, if like me, you get a call that isn't your department: "I'm afraid I'm not the right person to assist with this, but let me get some information for the correct team. I can put you through, but would you like to jot their info down just in case you need to get back in touch?"
A lot of it comes with time, at first you'll be using hold a lot, but eventually you'll get your call flow and the info will just be "there".