Just one thing before you go out and buy a new HDD or SSD...
While it is true, as SR-71 has indicated, that ordinarily you will be unable to boot to the OS from a USB externally connected drive, it can happen.
Now you would need to CLONE (not "copy") the contents of your present boot drive to the USBEHD and attempt a boot from the USBEHD. If you're lucky, (it's something of a crapshoot) the system will boot to the OS. Since there's nothing to lose by attempting this, you might want to give it a try. It sounds like you've never undertaken a disk-cloning operation before. If that is the case, do some Google research on "cloning the contents of one drive to another drive".
Understand that we're assuming all the data - including the OS - that you will be cloning to another drive is incorruptible. In other words, your present system boots & functions without problems. "If you clone garbage, garbage is what you get". Capiche?
The disk-cloning program we generally use is the Casper program, however, it's a commercial program costing $49.99. There are a number of freely-available disk-cloning programs available as you will see from your Google research. Casper does have a Trial Edition available - see - https://www.fssdev.com/products/casper/trial/