Why am I moving slowly when I'm not over-encumbered?

Solution 1:

In Skyrim, holding the shift key will make you walk instead of the usual jog the character always does when moving. This is useful when trying to sneak past an enemy, as it makes you harder to detect.

Pressing the caps lock key will toggle the walking state, but it's never really explained in game, so it confuses people who accidentally press it while playing. This is what happened to you, it's not you being overencumbered, just a slightly unknown feature of the game.

Solution 2:

As @DanmakuGamer stated, you might've gotten the "caps lock" button pressed. This will cause you to move slow. Make "caps lock" turn off so you can run.