In general, there are quite a few effects. For example, high pressure helium can cause high pressure nerve syndrome. It is characterized by tremors of the upper limbs and trunk, decreased concentration, decreased perception, drowsiness and stupor. It often occurs among scuba divers when diving to depths below 150 meters, as they breathe mixtures of helium and oxygen.
It should be said that breathing pure helium, like any other pure gas besides oxygen, is life-threatening. It blocks the access of oxygen, not receiving which a person begins to suffocate. However, due to its lightness, this gas can be used to replace heavier nitrogen in breathing mixtures. Due to the low oxygen concentration caused by the high content of helium, the person may feel dizzy, vomiting and nausea. If this condition continues long enough, a person can die from a lack of oxygen.
By the way, the increase in the timbre of the voice when inhaling helium is associated with a higher speed of sound in this gas, which is due to the higher speed of movement of molecules in it.
Under the conditions of the human body, any inert gas can be considered absolutely chemically inert. And this is not quite a tautology, since some of them, despite their name, are characterized by a fairly developed chemistry, for example, for xenon.
Nevertheless, the very fact of their inertia does not mean absolute harmlessness. Inhalation of pure helium can lead to asphyxia and even loss of consciousness. In addition, it is reliably known that all inert gases, especially xenon, upon prolonged inhalation enter the body into a state of anesthesia, which is apparently associated with their adsorption on the cell membrane. This slows down the transfer of ions through it and, as a result, inhibits nervous reactions.
As for the harm to the voice, then, probably, one can only guess, since hardly anyone has conducted a detailed study of such things. I think that once you inhale helium, you make your ligaments vibrate at frequencies uncharacteristic for them - this is unlikely to be very useful for them.
To summarize, it is worth saying that helium is certainly not harmless, but no one is breathes it daily, for ten minutes every hour. It's just one piece of fun. I dare to assure everyone that walking along a busy highway, you do much more harm to your health, and the notorious carbon monoxide is the least possible threat.