Why do car headlights and streetlights turn into large blobs instead of thin light trails?

The blobs result from the bright areas being extremely overexposed. So, quite simply, you need less light coming in. The ways to do that are:

1. shorter shutter speed (keeping ISO & aperture the same...I'm assuming you're operating in manual mode and can control those). You probably don't want to do that in this case, because it will decrease the "trail" effect.

2. smaller aperture (keeping shutter & ISO the same). But as you've said you cannot go any more on that.

3. lower ISO (keeping aperture & shutter the same). I don't know the specifics of this camera but guessing 100 is the lowest? So probably that's out.

4. use a neutral-density (ND) filter (all other variables the same). Given the above points, I think this is the only way you're going to improve things in this image. If your lens does not accept filters, you could probably rig up something using one of the larger square/rectangular ND filters and some rubber bands or some such. A Polarizing filter might help some; not so much because of the polarizing effect but because they also generally decrease the amount of light coming in...that is the main issue in this case.

As another poster mentioned, you could possibly change your angle to the cars so that they're not coming directly into your camera, but that obviously changes your composition so that may not be a realistic option depending on what you have in mind.