I don't get how the game reflects in any way on the statement...
The game was pretty nice still.

Pretty interesting premise, nice animations, sound FX and the music was pretty relaxing. Which coupled with the slow pacing was a little ... too relaxing at times. Could be more engaging with a bit more escalation. 

Since I don't have the book, I can't rate whether this is faithful to the original "what if?".  For the sake of fairness, I'll rate it a 3, right in the middle, for "xkcd-ness".

"I'm looking for feedback! Please let me know what you think. I want to make the game better."

I appreciate that!  I'll do my best to make my thoughts clear and helpful. :)

"Don't get sick!"

Too late.  (I am sick in real life as I type this.)

Anyway, let's get to the game itself.

The idea behind The Common Cold is interesting, though it isn't what the game itself says it is.  The title screen says that I'm playing this to find out "If everyone on the planet stayed away from each other for a couple of weeks, wouldn't the common cold be wiped out?"  But the game isn't about everyone being isolated, it's about making sure those who are sick don't stay sick enough to infect others.  

So that's quite misleading.  I started this game and immediately tried to keep people away from each other and scrambled to find out how I could isolate them (I thought I had to keep people behind the fences or something), but was confused when they resumed walking a moment later instead of staying put.  In order to gain clarity, I had to read the description--which also told me the basic rules of the game.

It's very hard to tell who is sick in this game.  There's a coughing sound effect, yes, but there are also 30+ stick people scattered on the screen at once (some of who walk offscreen with their legs poking out from the top), and the coughing animation is difficult to distinguish from the regular walking one if you're not looking for it; there's not enough visual information, so when someone coughs, I have no idea who it is unless I happen to be looking at them, and the stick figures aren't scattered too much on screen.  Not to mention that after they cough, they stand there in the same way that other stick figures just stand there when they feel like chilling out, blending in with the crowd and making it harder to cure them.  The obvious solution is to have some kind of signal above their head, and/or make the cough a certain color, like green or yellow, and/or playing an "alarm" sound, and/or having them walk differently after they cough.  Also, I'm playing with speakers, not headphones, so if the coughing sound effect is coming from a certain area audibly, I can't tell.

Which leads me to another point: Curing people is hard.  Not only because I can't tell who's sick, but because there's only one bed, and the game doesn't tell me the boundaries of curing people.  Is there a certain amount of time sick people need to stand by the bed?  Can I put more than one sick person in the bed at once?  If I put a sick person and a healthy person near the bed, will the sick person be cured, or will the healthy person get sick, or both?

And speaking of that, how fast does the virus spread?  That's not clear at all.  I assume there's a time frame of some sort, but I genuinely don't know.

I do like the music that goes with this game, though it can get a little tiresome after a while.  Picking up people is fun, but the "Oh!" that they say when you do is all nearly the same sound effect.  Some more varied sounds/lines would be nice.  There is a genuine charm to this game that I like, even if the sound effects get a tad redundant.

So yeah, this is a neat game idea, but leaves much to be desired.  As for a win condition, this is one that requires expanding the game a bit, but here goes:

--Once you reach a certain point, you realize that the cold won't stop infecting people, and you need to find a permanent cure.  In the next level, the player needs to look not only for sick people to cure them within the time limit, but also scientists in the crowd, who you bring to a lab (at the corner of the screen?) to find a cure for the common cold (and if the scientists get sick, you need to cure them too, which ticks away at the timer).  You need to survive each new level to give the scientists time to research, develop, test, and complete the cure.  Perhaps how fast/slow the cure is developed depends on many scientists the player was able to find, and maybe you have to bring people to the lab to intentionally infect them for research, and hopefully cure them in time before they infect the general population.

Hope this helps!  Please let me know if you have any questions about anything I said here.

You asked about a possible win condition; the question itself mentions "a couple weeks": you could have the win come after 14 days

I like the idea of simulating disease spreading. Maybe the winning condition can be eliminating infection at all. Or you can play the "dark side" a and your goal is infect all people like in Plague Inc.

Cool. I think the difficulty needs to be adjusted a lot though, it shouldn't be possible to pass a level without interacting at all. Might help the gameplay if you increase the rate of infections, but add more beds.

Neat concept on making an XKCD concept a game. Anyway one thing I do want to mention is I'm doing a review of design on the games in this jam so here's a shameless plug to my channel if you want to be notified of the vid when released: https://www.youtube.com/channel/UC7Vj46GGL9VMUvd4YTMtjXg