Engines are basically air pumps. Air comes in one end and exhaust goes out the other.
Air is high in oxygen content, exhaust is not.
Valves are used to keep air moving toward the exhaust side of the engine and preventing it from coming back.
When a valve doesn't close, it opens up a huge opportunity for oxygen-poor exhaust gases to be pulled back into the engine. Then this used-up air gets so far inside that it contaminates the intake charge for other cylinders, leaving insufficient 02 available to burn the fuel being injected (this is why the engine flooded).
More fuel continues to pour in, but can't be burned and at that point you have to do something like the choke unloader function. I cautioned you to lift off the throttle quickly for just this sort of reason; to prevent engine damage if a valve happened to be "swallowed" by the engine already.
You can't normally hear any mechanical noise when a valve spring breaks unless the damage is already done. I'm afraid this is one of those times.
You'll need to get a second opinion and an estimate, but steel yourself for a cylinder head replacement and probably one piston.
A second possibility for the noise you're hearing is that a steel valve seat came out of the aluminum cylinder head and that's what is bouncing around in the cylinder, making noise. The effects of a dropped valve seat are very similar to a broken valve spring in that your exhaust now mixes with the intake, but it might be a bit more expensive.