Alcohol inks might be dangerous for you if not used correctly and if precautions are not taken while working. Here are few things to keep in mind:
Do not work with alcohol inks if you are pregnant: Nobody knows exactly what the harmful effects of inhaling alcohol fumes could be on your baby, so it's best avoided. Try watercolors instead.
Do not let children work with alcohol inks: 16+ years is better age for working with alcohol inks because we can expect elder kids or adults to be careful while working with inks.
Work in a ventilated environment: If possible, keep your doors and windows open while working with inks. If the weather is not good, at least run exhaust fans or air purifier to get rid of the fumes faster. If you work at home, please keep your kids and other family members away while you are working.
Wear gloves: I use simple surgical gloves or latex gloves to protect my hands. Alcohol inks will stain your hands and do not come off easily if you are not careful.
Protect your eyes: If you have sensitive eyes, I recommend wearing a protective eye wear as well. Sometimes, inks might splatter when you open a new bottle; wearing glasses can prevent them from going in your eyes.
Wear a mask: This is the most important product that you must buy if you plan to work with inks regularly. I use a 3M Medium Half Facepiece with Organic Vapour/Acid filter cartridge. Once I wear it, I cannot smell the alcohol at all. You may find similar masks, but do check that you should not be able to smell the fumes. I wear the same mask while varnishing as well.
And lastly, do your own research. Your body might be more sensitive than other. Do not rely on others if they tell you it's safe, find out on your own and read about it, so that you are well aware before you get into this artform.
Thanks for reading. Stay safe.