The app store says I haven't purchased any apps but I have

Hi I was wondering if anyone can help me

Basically my MacBook Pro's hard drive recently got corrupted and I had to get a new one. Most of my files were saved, thankfully, but all of my apps were deleted. I've tried to re-download them from the app store but when I sign in, it tells me that I haven't purchased any apps, which isn't true!

My main concern is Pages, to be honest as I am a university student so having a word processor is kind of essential! And being a student I don't really have a spare £15 to buy something that I've already bought.

I may have just used another Apple ID to purchase all my apps for my Mac, but I have no idea what that was, except for the fact that I probably used the same email address for the Apple ID I know and the one I don't

So to make a long story short, does anyone know how to a) restore my purchases, or b) find my other Apple ID?

Thanks for your help in advance! 🙂