Spitting or coughing up blood days following a neck or throat accident is not typical and can be a sign of an internal injury that must be examined immediately. I'd have you see an ENT doctor as soon as possible, even privately, so you can stay away from the hospital environment where they may probe the cause more forcefully. You can just tell them you've had really bad pain or trauma to your throat by accident (e.g., bumping it off something or you fell) and you've been spitting up blood or coughing since. The key is you need to be checked out soon because some of the complications are worse without clear significant early symptoms.