Normally you would include a an object known to be white in each frame. There are special things for this, most commonly White-Balance Cards Then, you use the software to pick the WB from that point. Repeat for each image and the colors will now be the same.

For levels, I suspect you mean that you got a different exposure. To fix that, you must shoot all the set with the same EV, which is easiest to do in M mode by selecting an aperture, shutter-speed and ISO and not changing this between frames. In any other mode, the camera will choose an exposure based on the content, so different painting are likely to give different results.

The same thing for WB can be done for exposure using a gray card. That is an object which is known to have a certain reflectance, usually 30% grey. You include that in each shot and then you can use Photoshop to set levels by sampling from a point on the grey card to be the mid-point.

NOTE: Unless you did the above, swiveling the camera will not solve your problem. The camera will see something different in each frame and therefore will pick different exposure and WB settings. This happens even is shooting RAW where the WB is not baked but usually stored as default.