My 2012 MacBook Pro fell and it now makes a clicking noise and shows a grey screen on startup. I'm afraid the hard drive is damaged. Is their anyway to still back up my hard drive even if it doesn't turn on all the way?

So my late 2012 MacBook Pro was sitting on my desk when the desk collapsed. The computer fell with it and I was quite scared at the moment, but thankfully I opened it up and it worked perfectly fine again.

I was later watching a YouTube video and pressed the back button. The screen then froze, and I could not force quit safari. Then this weird clicking noise started to happen. It was coming from the right of the trackpad. That's when I decided to force shutdown the computer with the power button.

I let it sit and then decided to turn it back on. The clicking noise then came back and there was just a blank screen on the boot up. Eventually a grey folder with a question mark started flashing on the screen. That was all it did so I decided to turn it off again.

I'm going to take it into the Apple store ASAP, but I'm curious if my hard drive is damaged and if I will need a new one, which would erase everything on my Mac. So I was wondering if there is anyway to back up the hard driver even if it doesn't boot up all the way, or turn on the computer all the way.

P.S. I have never backed up my hard drive so I wouldn't know what to do.