Can you tell us the exact model of your lens? "Kit lens" covers a broad range with Canon.
I have the 18-55mm and the 55-250mm
Neither of those Canon lenses are "terrible".
In fact, for a kit lens which is thrown into the deal at such a low cost, both are quite good when it comes to image quality. I think even non-Canon shooters would have to agree with the fact Canon has done their users a great favor in how much quality they have packed into a lens which costs so little to own.
There are several other (rather high priced) camera manufacturers who, IMO, could take a lesson or two from Canon on how to provide good glass at reasonable prices.
Most student photographers would probably be somewhat hard pressed to notice a significant difference in resolution between a kit lens photo and a prime lens photo in most instances when your kit lens was either of these two examples. Either lens scores quite well in consumer or "pro" reviews.
I would encourage the op to check out the reviews and comments which are available for either individual lens. I suspect you would learn a few tricks and find a few tips about how to achieve the best results possible with either lens.
This comes down to one of the very first rules of better photography; learn and know your equipment and how to use it to your best advantage.
Both feature Canon's image stabilization circuitry which should provide an effective safeguard against camera shake when pressing the shutter release.
Yet this is still my first suspicion when I look at the image examples. Which leads me to think the op has either defeated or somehow disabled the image stabilization system.
I cannot detect an aperture issue since there are no planes of in focus imagery in either shot.
Obviously, subject movement would not have been an issue in the second example. The building is out of focus and for that to happen as a result of subject movement, I would applaud the op for standing still while an earthquake of that magnitude was occurring.
In other words, subject movement is not a cause of blur for either shot. We can logically eliminate that from our list of possible causes.
I do suspect someone who has convinced themself a problem exists in aperture will have played around with aperture and the lens itself to the point it is poorly adjusted. However, without any plane of in focus image in these examples, I simply cannot see that aperture is the cause of the blur.
Let's, for now at least, remove that from our logical conclusion list of causes.
I would suggest the op do a bit of kitchen table research with his camera and its owner's manual at hand. Do make an effort to understand focus points and how autofocus operates on your camera.
Double check your menu settings for focus systems and be sure you have the camera set to its best option for any one photo. There are distinct reasons why you will change focus points for any one shot. There are very distinct reasons for using the various focusing systems on the Canon as each photo dictates. If, for example, you are using a tracking focus system best suited to shooting images of subjects moving towards the camera, you may be catching the camera at an out of sync point where focus should be set and immovable.
Therefore, read about, understand and implement your focus systems correctly.
Understand what the camera is telling you when it flashes a signal in the LCD or viewfinder which suggests the shot is not in focus. It's highly unlikely there would be a focus issue with both lenses unless the problem began with the camera or its user.
Certainly, make sure you have the lens set to auto mode and that the switch is fully engaged.
Understand how each lens operates its manual focus override.
The general blur in these photos somewhat suggests you might be holding the camera in a manner that places one hand on the lens focusing ring and you are slightly shifting the focus manually just before snapping the shot.
This would be another case where a tripod mounted photo would indicate a logical path to a resolution of the problem. Do the two tests I suggested earlier, the tripod mounted and the continuous shooting mode tests, and when using the tripod, don't touch the lens itself after you've mounted the camera.
When shooting the continuous mode shots, focus the lens, check for accurate focus and then do not touch the lens. Hold the camera with a somewhat open palm method where your fingers are not in direct contact with the lens itself.
Even with the camera's image stabilization assistance, the problem would seem to me to still be either in the way the user is releasing the shutter or a matter of not understanding and, therefore, not properly employing the autofocus points/autofocus systems.
Add to this now the possible movement of the lens' manual focus override and I feel you have, at the least, logically narrowed down your possible causes to a reasonable number.
Any or all of these issues are common to student photographers.
From there, once you have conducted the tests shots, you should be in a far better position to pin pointing your cause. At that point it is only a matter of time and practice - along with attention to detail - which will lead you to a better result.
Your camera and your lenses are perfectly capable of taking sharp photos.
There is a very slight possibility you have a defective camera but I really think that not to be the case here. You know how the camera has been handled and whether it might have suffered some sort of damage from a fall or sharp knock. That the camera would react to average wear and tear is not average so it is on the far end of the possible here IMO.
However, if you know someone with good photographic skills, ask them to take a few shots with your camera. Between their results and the tests shots I've described, you should come to a resolution rather quickly.