I do not know that specific camera, but generally sensors will have a pattern of thermal noise which is not uniform. The "Long Exposure Noise Reduction" feature, if your camera has it, is intended to offset this somewhat. Enabled, it does much as you did, taking one image with the shutter open, and one with the shutter (or in your case the lens cap) shut. In camera it would then subtract, numerically, each pixel of the latter from the former. The process is not perfect; noise is statistical in nature, and not perfectly repeatable. By that I mean that a specific pixel will not have the same value from such a "dark" frame twice, but what does happen is that some areas tends to be brighter, repeatably, in the same spot when taken under the same condition. Doing this "dark frame" subtraction thus selectively darkens the area.

One way to think of it, which is not far from reality, is that each pixel is a well that becomes more full as it exposes. Noise, in a sense, is garbage that is in the well and artificially fills it somewhat. The dark frame adjusts each pixel trying to get it back to an empty starting point. It is much better than just darkening the area, as that is proportional -- you are darkening the garbage instead of removing it, in a sense.

The dark frame subtraction (aka Long Exposure Noise Reduction) is also one of the few settings that affects a "raw" image in most cameras, high ISO noise exposure, for example, is not applied to the raw image. Long exposure noise reduction is.

Try turning on Long Exposure Noise Reduction. If you are curious about the technique, including being able to apply it manually, search for astrophotography and "dark frames", it is a very common practice there. It is also useful to do manually if your camera does not support it in camera, or if you need a lot of images in the same conditions and do not want to wait for a 2nd exposure for each one.

To your original question - did something you did cause this to be worse? My guess is no, but without some before and after shots, no way to know for sure. But what you posted does not look that unusual. Some cameras are better than others at producing less noise, but all are going to have some sort of pattern like this if you push hard enough to see it.