I recently won in an Official White-Yellow Belt Katana server, and my account details on the forum say I have 10 TC. But the in-game ToriShop says I have 0, and won't let me buy anything that costs 10 TC or lower. So, how do I fix this? Also, if it helps, I use Steam.

Must be happening because the item.dat file in your custom folder hasn't updated yet. Try switching to Free Play or joining a multiplayer server and going back to Torishop, that should fix it.
-----
edit: added a fix to torishop, it would force update your qi/tc on launch. Will come with a next update on steam.