Of course, that neglects the fact that, if you were actually travelling at c, you would experience no time whatsoever.
As in, the beginning and the end of the universe (or at least your emission and absorption, if you're a photon) are instantaneous to you.
So to answer the question, no you wouldn't see your hi-beams come on, because there's NO TIME in your reference frame. But theoretically... [sigh]-sure. You would see your hi-beams come on just fine. But it's kind of a non-question, since it presupposes that time (and hence, change) exists at light speed; as in, it doesn't even make sense as a question.
And, as already stated, an outside observer would measure both you and your "emitted" photons traveling at c in their reference frame; partially or completely because you are in a completely timeless "freeze frame" state relative to any non-lightspeed observer.
That's the easy stuff. You really want to cause brainhurt? Look up the "ladder and barn" paradox. It notes that objects shorten as they approach lightspeed; so let's say that you're carrying a ladder going so near to c that your length is cut in half to an outside observer. Thing is, you're still your "normal" length in your own reference frame... Now let's imagine that the barn is only as deep as 2/3 the length of your ladder. An outside observer would see you get all the way into the barn before you struck the back wall (relativistic explosion notwithstanding). You, however, in your own reference frame should see yourself only get partway in before you strike the back wall.
So which happened? Both? Neither? In the universe we know, only one should have happened; you either got all the way in, or you didn't. Now cue a LOT of handwaving by physicists that both A)ties your brain up in knots, and B)basically says "We dunno.". It's a NASTY one, and probably means that we don't understand the relativistic universe as well as we thought. My theory is that the universe "flattens out" relative to a lightspeed observer, so they both see the same thing happen (it fits) in the same way that time "flattens" to nothing at you approach c, but I'm not a physicist- though it does solve the problem, and kind of makes sense inside of the framework.