When I'm in any room, a few seconds later, my mouse continues to run to that direction, I didn't press the chat bar or anything.

Same as text; I didn't press the screen either.

What's going on; and what can I possibly do?

You might have locked on a key, either refresh, retap whichever direction it keeps on going (left, left key or a e.t.c) That should fix it

Usually caused by, holding left/right and switching tabs, which would normally lock the ingame key. I think.

^ I've tried that but the bug keeps going.

(refresh)
(bug keeps happening)
OMG WHAT CRUEL WORLD I LIVE IN

Well I think you ran in a direction and then clicked the chat box and let go of the direction key.

^ No, that's not what happened.