I wouldn't dry burn cotton. And I wouldn't use a coil that's not cotton, so..
Nobody dry burns cotton. Or if they do, they only do it once. Cotton is especially nice because it allows your coils to last longer - you can rewick!
Your coils will take on added resistance when first fired up, and again as the coil becomes gunked up. If you don't presently dry burn, that will explain the initial bump of 0.1ohm, since the coil wasn't "broken in" first. The second bump is almost certainly from your coil getting dirty, especially on high VG or dark juices.
Now, if your coil is showing different readings erratically, that's a problem to be dealt with immediately, since it signals a short or a loose connection or any number of nasty things.
My best suggestion is simply to clean your coils. Get some cotton for rewicking and you're off to the races. I prefer the dry burn method myself, but you can absolutely avoid it if you want, by washing the coils under hot water (just take the base out and let it soak). If you use a lower gauge wire, scrubbing the coils will really make a difference, but you do risk warping