http://periodictable.com/ZincSafety.html
So what's the worst that can happen from exposure to zinc, and can it cause hidden long term effects?
When zinc is raised to a high temperature (at or above its boiling point around 900C), it burns and forms zinc oxide smoke. Like any kind of smoke, zinc oxide will irritate the lungs, leading to difficulty breathing: This is not a dangerous situation and it clears up immediately when you move away from the source of the fumes. People exposed to high concentrations of zinc oxide over a prolonged period of time can also develop a condition known as the "zinc chills", "metal fume fever", "brass-founders ague", or a number of other colorful terms. This involves fever, tremors, and other unpleasant symptoms.
However, metal fume fever, which is rarely seen these days, is a purely temporary condition that clears up without any known long term effects or complications. It's certainly nothing to laugh about, but the maximum downside to zinc exposure is fever and shakes that go away and then you get better. It's not like lead or sun tanning that can have life-threatening consequences down the road, or like carbon monoxide that can kill you on the spot.
And you can't even get zinc chills from melting and casting pure zinc.
Welding galvanized steel generates zinc fumes because welding happens at very, very high temperatures: The zinc plating for an inch or so in every direction from the weld is burned off in billowing white clouds of zinc oxide. Anyone who has learned to weld will have been warned many times to wear a special mask when welding galvanized steel, and that's a good idea. I use one always when welding galvanized plate.