Why have I become invisible?

After Brelyna in the College of Winterhold "experimented" on me, I became invisible. Now I am unable to see my character at all. Is this just a glich; is there anything I can do short of starting a new game?

Edit: None of these seemed to work for the OP, but I'll leave them here as suggestions for those experiencing similar issues.

For the why, well, I have no idea (aside from "oh, Bethesda"). But I had a similar issue with a spell effect being permanently attached to my feet. It generated smoke, so my sneaky little thief looked something like Smoke from Mortal Kombat. I gamboled about until it finally resolved, I believe due to transformation into a werewolf. Your problem is due to either opacity (most likely) being set to 0 or your character model being non-existent (unlikely IMO).

There are several solutions I'll suggest:

Become Ethereal:
The Become Ethereal shout should fix any opacity issues when it ends. Here's a YouTube video from a user with a similar issue. Although it ends with the person just reloading a save and exacting revenge, the user claims that the suggestion to use Become Ethereal repaired the problem.

Become Ethereal's Words can be found in Lost Valley Redoubt, Ironbind Barrow and Ustengrav. If you can handle Hagravens and a few Forsworn, Lost Valley Redoubt's Word Wall is outside and probably the quickest.

There are also unique potions that let you become ethereal, called Philters of the Phantom. You can find them in a quest in Shroud Hearth Barrow, near Ivarstead. It's possible that an invisibility spell or potion will have the same effect, but I haven't tried that or seen it done.

Console (PC only):
Open the console (~ or whatever's above tab and left of 1) and type

player.setactoralpha 100

If that doesn't work, there's

sexchange
sexchange

It should force your character model to, uh, rebuild.

Werewolf:
Transforming to a Werewolf and back will also force rebuilding.

I'm dealing with the Breylin glitch too - now my character is invisible, and I don't have a save to load.

I tried the werewolf and no dice. Instead of walking and trying to get all the shouts to become ethedral (and doing all that while invisible which sucks), I decided to try my own thing.

So first invisibility potion, then I walked in a door while still invisible. I could see my weapons but nothing else.

Then I used a appear spectral (like a ghost) and you could see him but ghostly. I walked outside, waited for potion to wear off and - boom fixed - I can now see my character again!

I did some research a while ago for my own purposes and it turns out that using Become Ethereal and then fast traveling RIGHT after using it will you turn back to normal. This also works with the phantom potion everyone is talking about (Philter of the Phantom? Look it up). Results can be varied though, sometimes fast traveling is not needed, sometimes it is, and sometimes just using an invisibility spell works too. Hope this helps.