Are you sure you bought it? Has your Water Point count be reduced?
I only see the Summer '18 Ears, Ice Cream, Scarf, Striped Bikini and Tail in your wardrobe.
Unfortunately I don't have access to event currency/shop logs, so I cannot check whether you the sale didn't go through or whether you lost Water Points and did not get the hair or whether there was some other error.
Starkad will have to look into it as he has access to this data.
Unless your Water Point count has not been reduced? You have 1636 water points at rank 5 and you already bought a couple of event items, so that doesn't seem to unreasonable.

But it is in your warrobe now. It's an item you can used and equip in your wardrobe like any other item. Expect for hair from the cutting crew, where you have an option to purchase it as a permanent wig to keep in your wardrobe or just temporary change your hairstyle, all hair items are items that go in your wardrobe and have to be equipped.