Is a glass arrowhead possible? Yes. Using modern glass, an arrow has nearly the same penetration as a modern steel broadhead arrow, when measured using gel powder.
However, in our world, this is not very practical. Forest glass was the main type of glass made in Europe in the medieval ages, it was low quality, prone to chipping and cracking. Transporting, storing and marching with glass arrowheads would damage them, making them less useful than metal ones.
The other problem is making them. Glass making was expensive. Cheaper to use bog iron, melt down old metal items, or dig iron out of the ground than go through the trouble to make glass.
If people were low on metals, they would turn to natural glass like obsidian and flint. They're cheaper, easier to make, and not as fragile as the man-made glass of the time.