As you have worked out, what you are seeing is an artifact of your eye: there can be similar effects from fog &c, but these effects would not be eliminated by masking the bright source, and would indeed become more visible as your eye would no longer need to deal with the bright source, for the same reason that people mask the disk of the Sun to see the corona.
The generic name for these effects is probably 'flare', and it is more commonly discussed with respect to cameras than eyes (hence mention of 'optical system' below) but there are a lot of variations with different mechanisms:
- flare is caused by light reflecting off surfaces inside the optical system (including lens surfaces in particular), causing various, usually very distorted, ghost images;
- glare, or 'veiling glare', is caused by light scattering from things inside the system, resulting in a completely diffuse pattern of light across the image area;
- bloom is interesting, and is a diffraction effect caused by the finite size of the lens, which means that it must inevitably produce, essentially, Airy disks for point sources, and these disks get added together to produce a 'halo' surrounding things.
Flare and veiling glare can be reduced by careful design (this is why the insides of camera lenses are matte black, for instance, and why lenses have fancy coatings), bloom is harder to deal with.
Flare and veiling glare are often caused by light sources outside the image area: light gets into the optical system at some angle greater than the image, and then bounces around resulting in flare or veiling glare.
Flare is a very characteristic effect, and is often associated with older lenses, and intentionally introduced to give a particular look: the 2009 Star Trek film is a famous example.
See below for a second cause of a bloom-like effect.
It is important to understand (but, I think, not often realised in the camera-lens-appreciation field) that these effects are always present: lenses are essentially linear things, so if a lens (eye) suffers from, say, flare, it always has it: the ghost images are always present.
What stops them being visible is that they are far less bright than the real image, so they are typically simply not visible as they are outside, or nearly outside, the dynamic range of the sensor (your retina here).
The case when they become visible is when there is a very large range of brightness either in the image or, in the case of the first two, near enough the image area that light gets into the system.
- In the case of flare & veiling glare, a bright light source (often the Sun, or street lights at night) outside the image area results in the ghost images or diffuse grot becoming significantly bright with respect to the image. This causes either the visible artifacts we love (or hate!) or, in the case of veiling glare, a general contrast reduction in the image (which will often remind you of 70s movies as a result...). Avoiding these effects is what lens hoods are for, of course (lens hoods had apparently not been invented in the 1970s).
- in all three cases, if the bright source is inside the area it generally becomes impossible for the sensor (film / digital sensor / your retina) to cope with the dynamic range of the image. The solution which is usually best in this case is to allow the bright areas to become burnt out -- they are completely above the dynamic range and appear as pure white -- while the darker areas of the image are kept within the dynamic range. That's often the best answer because the surface details of, say, a street light are less interesting than the hideous monster which lurks in the shadows beneath it (see note below about eyes). This then has the same result: the ghosts, veiling glare and bloom are now relatively bright compared to most of the image, and become visible in the image.
Significantly, only the second case applies to bloom: for bloom to be visible there needs to be an enormous dynamic range in the image, or very close outside it, because bloom is a 'short range' effect on the image: it always surrounds its source. Bloom is often used in movies involving aliens for some reason (perhaps only in my mind).
In your case, I think that what you are seeing is bloom: diffraction effects from very bright sources which your eye is allowing to become burnt out in order to be able to see the rest of the scene. If you mask the source, the bloom goes away, as you have seen. As I said above, the eye always has bloom (and the other effects): you just don't see it normally as it's outside the dynamic range of your retina. Additionally, in the case of eyes, I suspect there may be a lot of active correction going on: I don't think our optical system is as good as it seems (single-element lens, for instance).
It might also be halation: see below.
I apologise that this answer is written mostly as if eyes and camera lenses were the same: my interest is mostly in camera lens design and I have not corrected heavily enough. I believe the optical considerations are the same, however.
An alternative bloom-like artifact: halation. Sensors don't absorb all of the light incident on them (or even most of it). The spare light can end up reflecting or scattering within (usually at the back of) the sensor, and then being detected. This is called 'halation' because it causes a 'halo' around bright objects, in a way similar to bloom. Unlike bloom, halation can be largely dealt with by good design (or evolution): films for instance have 'anti-halation' coatings on their back side which try to reduce reflection and absorb light. These coatings are sometimes exciting colours (bright purple for Kodak B/W stock), and wash off during processing causing alarm to people doing it for the first time.
A note on eyes and bright sources. I said above that it was usually better to configure the system so that small bright sources were allowed to be burnt-out: completely above the dynamic range of the system. That's fine so long as they are not too bright: if they are too bright they can physically damage the sensor. For film this is not a problem unless you end up setting it on fire; for digital sensors it destroys the camera; for your eyes it permanently damages your retinas. Retina damage is undesirable, so generally the system will try to avoid this by dramatically reducing the sensitivity (by closing your iris and ultimately by closing your eyes completely) when there are very bright sources in the image area, even when it means not being able to see. This is, of course, a problem when what you don't see is the hideous monster lurking in the shadows: that is why they lurk there, of course.