When on your profile it says that you have chests available, that means that you are currently able to earn a hextech chest, not that you actually have any. In order to earn one, you or someone in your premade party needs to earn an S- or better grade at the end of a match. When this happens, you will earn a chest.
Also, something important to keep in mind is that you can only earn one chest per champion per season. Once you earn a chest while playing as a certain champion, you will be unable to earn anymore chests while playing as that same champion for the rest of the season. If you keep playing the same few champions over and over, you will only earn a small amount of chests.
For anymore information, you can check out this guide here: https://support.riotgames.com/hc/en-us/articles/207884233-Hextech-Crafting-Guide