In Game of Thrones, dragonglass seems to be used as weapons against White Walkers.
Why don't they use dragonglass swords instead of daggers?
Dragonglass, if it is like our obsidian, would be too brittle to make classical swords. But that does not mean that they are limited to arrowheads, spears (by the way, the first picture seems to show spear head and not arrow head) or daggers. The lack of good metallurgy gave a good incentive for mesoamericans civilizations to use obsidian
They used, for example the macuahuitl, which is a sort of wooden sword with encrusted obsidian blades.
I don't know of any other way to make weapons from obsidian that have the same properties as a sword. Whether or not they could find a way to make swords with dragonglass (by making macuhatil or through some other means) is pure speculation though.
Also, keep in mind that they just started the extraction of obsidian, so they need more time to make proper weapons. It will not be an easy task as a blacksmith is not used to make dragonglass weapons.
Here's Tormund's Dragon glass weapon for an example:
Dragonglass (obsidian) is a brittle material. Daggers are short and less likely to break. Furthermore, obsidian cannot really be forged. You're effectively breaking shards off and hope that one comes out roughly dagger-shaped.
So swords would be prone to breaking or shattering rather quickly. And it's quite difficult to get something sword-shaped from obsidian since that'd require a large elongated pointy shape, instead of just a small elongated pointy shape.