Based on the pictures I think it may have to do with ther angle of your hand when you're doing certain punches.
I know when I do hook punches, a will sometimes hit with the second knuckle on the index instead of the first knuckles. Also, rarely I will, for seemingly no reason at all, not tighten my knuckles enough before the impact and strike with the secon knuckles instead of the first with straight punches.
Also, there is nothing wrong with just using handwraps. It helps condition the hands/wrists, and build scar tissue in the dermic layer of the skin(the skin under the surface)which actually prevents bleeding in the future(will cause poor perfusion--cold hands). However I would recommend doing it both with and without handwraps. When I do a session on the bag, I will use heavy bag gloves, then just wraps, then gloves again, almost in a cross training mindset. I do the same when I do GnP on a bag.
The whole point being, you're kind of okay the way you are. If I were you I would work on my form with any punch where you hit with the wrong knuckles, unless you are deliberately hitting with certain knuckles.
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