There are a few other possibilities I can think of. 

Playing the violin involves hair, wood, and rosin, all of which are affected to some degree by changes in humidity and temperature.  They all have their effect on the sound of the instrument. 

Your "ear" also can change a good bit, even over the first few days.  Especially the first few days, in fact.  You have probably been listening to a lot of recordings or videos of various players that sound great, and so the expectations you have of how it should sound when you play go up.  That is natural, and a good thing in the long run.  But often discouraging in the short run.  It is why a lot of people give up in the first few weeks of trying to learn an instrument.

I have been playing various musical instruments for almost 40 yrs now, and I can tell you that unless something really catastrophic was going on, like the instrument literally falling apart in my hands, I wouldn't jump to the conclusion that the tone of an instrument was "deteriorating" over just a few days.  I'd want to play it every day for a couple weeks before jumping to a conclusion like that. 

One can certainly hear some real changes over the first few days, though.  They are not imaginary.  They can be due to weather, as already mentioned.  With new instruments, they can be "settling", which is the mechanical process of the parts of the instrument adapting to the stresses of being tuned up and played.  

There is one possibility, though, that comes to mind with a new violin.  Take a thin piece of paper, and see if you can get get it to slide in between the "feet" of the bridge and the top of the violin at any spot.  If you can, then the bridge isn't sitting flat, and that can make any violin sound less good.  With the tuning up and re-tuning that is usually necessary with a new instrument (or after a string change) it is not unusual for the ridge to start leaning a little, and the feet end up lifting off the surface in one or more spots and that can definitely affect the sound adversely. 

You may notice that none of the possibilities I have mentioned have anything to do with whether your violin is expensive or not.  That is because any of these things could happen just as easily with a violin that cost as much as a house as they could with one that cost less than 100$.  Especially for a beginner in their first few days of playing.  I'm not saying there aren't some likely quality differences, but there is no reason to just assume that the instrument being inexpensive is actually the problem.

Now, you didn't mention how you feel the instrument sounds different.  If it sounds thinner, or muddy, or there's a buzzing sound, or it is raspier, these would all indicate different possibilities.  Just starting out, you may not have figured out yet how to record the instrument, but even some pictures (full view and close up) could help.  Some of our members, like Fiddlestix, have an eagle's eye for spotting little problems.  They may be something that can be easily fixed, like the bridge not sitting quite flat or in exactly the right spot, or in some cases they might actually be something serious enough that it would be better to find out now while you can (hopefully) still return the instrument and get another.

How much you can tell/show about the problems you are having with the sound does affect how much help anyone from a place like this forum/community can give you.