Phone cracked the bottom, touch not working and half screen is black.

I have grandchildren and as a result have far more experience with screen replacement than I would wish on anyone.

That being said, yes, a simple screen replacement will almost certainly fix you right up; unless you're seeing other problems with the phone right now, there's no reason to expect any other issues. The screen and digitizer are fused together and it seems the drop damaged both, affecting the touch input and the display so a new screen will give you both functions back.

Poco X3 Pro Screen Replacement - iFixit Repair Guide

I usually start with places like Amazon, eBay and AliExpress when looking for replacement parts; here's the first one that came up on Amazon that should work.

Amazon.com: Screen Replacment for Xiaomi Poco X3 X3Pro X3NFC, Display Screen Digitizer Assembly Phone LCD Screen Replacement Kit with Repair Tools : Cell Phones & Accessories

Good luck; let us know how it goes! Feel free to ask if you run into problems or have questions.