What i wish to ask is how would the world change over the course of a week(I plan to finish the plot in a week.) other than the world becoming cold?
Other than getting cold it will get dark. That may sound trivial but animals are mostly hardwired to operate on a diurnal cycle of 24 hours and their body clocks get totally out of whack (to use a technical term) when you deprive them of a regular day-night cycle.
For humans, ignoring the cold, a couple of days of this will have psychological consequences for most people. Your sleep pattern goes wrong for a couple of days and you're soon suffering. Humans do not thinks rationally or well when their sleep pattern is disturbed. Daylight is an essential ingredient in your psychological well being. This has implications for a break down in the so-called social fabric.
Now it gets cold, and this has practical consequences. Frost won't clear and will build up. Snow will fall and won't stop (at least in a week). So transport infrastructure, mostly dependent on ice-free and snow-free conditions, will break down rapidly. In some countries they can cope better than others with this, but in most temperate climates and particularly in countries where snow is a rarity this will be devastating.
That has severe implications for food and fuel supplies. By the end of a week stocks would be running out - you live in a world largely based around daily-demand with constant delivery streams.
A week is not long enough to cripple industry, but a week is long enough to see supply chains broken.
It would take a great deal longer than a week to design a replacement infrastructure (if that's possible) capable of supporting transport in a "Big Freeze" like this. It would perhaps take six months to a year to develop the required infrastructure and implement it well enough to sustain major populations reasonably. This is beyond the time scale of your story.
Darkness brings other things - criminals. It's not that they don't operate in daylight, of course, but they like the dark. Criminals, particularly those robbing food stores and other items for resale on a black market, will increase. Everywhere martial law would be introduced, but martial law won't necessarily stop this increase, but will blunt it a little.
Legally states of emergency would be declared everywhere. Civil liberties would be taking a back seat.
Politically people won't necessarily believe that this is a permanent state of affairs. This will complicate handling the problems and may result in major political unrest. There are even people daft enough to think their governments are responsible for this state of affairs or that they can do something to turn the Sun on. This would create some unrest, how much is difficult to say. Again martial law would complicate this and not necessarily solve the problem - if history proves anything it's that troops on the street doesn't generally stop crime or protest.
So rapid political chaos. In some places the military would forcibly take over - maybe to try and do the right thing, maybe just as an expedient because in some places the military are just looking for an excuse anyway.
Humans are into the blame game. A lot of effort will be made trying to find out who to blame (i.e. your political enemies are to blame - make everyone else believe that), and not as much will be done to try and cope. Look at Brexit - lots of "whose fault is this" in the UK and very little "here's a sensible plan" Unfortunately that approach is not unique to the UK - lots of countries fail to deal with problems and play the blame game. The first week in a lot of democracies will be spent playing the blame game before the cold and dark (and possibly political necessity) finally make that pointless.
So lots of running around like headless chickens with the same end result, I suspect.