Yes you can install a new screen, its not too hard but be sure to get the EXACT model for your laptop, you can usually find them on Amazon, eBay or a local computer store, although that will be the most expensive option.
if youre not comfortable doing it yourself, a shop can replace the screen for you, but its pretty simple. Get a decent set of mini screwdrivers to match your screws, otherwise you could strip them.
quite often when you take your damaged screen out there will be a QR code to scan or a serial number which you can use to figure out the proper replacement. Dont try to use anything with a different resolution, it may work a few times but not for long, and can cause many more troubles.