I assume you mean in one of the arteries or veins, since other places in the throat wouldn’t cause the situation you’re asking about.
Not that it matters, because the first aid is the same. Pressure, pressure, pressure. First and always, apply pressure to slow bleeding.
If it doesn’t hurt like a motherfucker, you aren’t using enough pressure. Seriously.
Position is not important, as long as you can sustain the applied pressure. Being face down or face up isn’t going to change the blood loss in shut way that matters. Pressure will.
Unless the wound goes through an artery into the trachea, the blood being inside is irrelevant. Pressure is relevant because it controls bleeding.
Even if the wound *does* go into the airway, position doesn’t matter, pressure does. Pressure controls bleeding, internal or otherwise.
If the wound *doesn’t* damage the carotids or jugulars, you still apply pressure. And you apply just as much pressure. The bleeding won’t be as dangerous, but you still need to control it. Guess what controls bleeding. Exactly! Pressure!
What do you use, and how do you use it to apply pressure? You use what you have; hands, a shirt, bandages. You press down hard, ideally with the palms until bleeding decreases. Then press some more. As long as the person can breathe, keep pressing. Then maintain that pressure until help gets there.
That’s the only thing you do before applying pressure, call for help.
If life were perfect, you’d have highly absorbent pads to apply pressure with. But any fabric is better than hands, and hands will help more than nothing at all. Clean fabric is best, but if you have to choose between a slightly dirty shirt you’re wearing and using only hands, sacrifice the shirt. The fabric would have to be *very* soiled before it was less desirable than bare hands.
That’s because the fabric distributes and applies the pressure more evenly. It also absorbs and distributes some of the blood.
If all you have is a roll of paper towels they can work.
About the only absorbent fiber based material that *won’t* work is toilet paper because it’s designed to come apart when wet.
If the foreign object is still in place *don’t fucking remove it*! Just don’t, period, no exceptions. The extremely niche cases where removing the object is actually better, you aren’t going to identify without training, so don’t bother.
You stabilize the object instead. You won’t need to apply pressure most of the time because the object itself will reduce blood flow. If there’s significant bleeding, stabilize *and then* apply pressure. Just apply the pressure *around* the object rather than pushing it deeper.
There ya go. That’s what you do if stabbed.