I have recently acquired a sweater, the problem is that the inside in composed of cotton and as it's new, I always have little pieces of coton remaining on T-shirts I wear with, which is annoying.
You can try using a lint roller, it's meant to remove dog hairs from clothes but should also remove what you describe as "little pieces of cotton".
You can brush the inside of your sweater.
A hair brush can be used but there are special brushes with short hard hairs which are specially designed for brushing clothes.
Brushing will take away the loose ends of fiber, which should help against pilling, and it will take off the pilling which is already there.
Be careful, try it on a bit where it will not show, like the inside of the arm in the armpit.
I bought some hoodie, and the inside was a big pile of mess of white fibers (I have no idea if natural or artificial). You can imagine the amount of fluff I had on all the other clothes i wore beneath that hoodie.
I took a simple brush, turned the hoodie inside-out, and brushed the "hairs" away, until most of them were gone. Literally, they can never be all gone, but I made a rough decision about when enough was enough. Then I strongly shook the hoodie while still turned inside-out, to remove all loose fibers. I turned it back out-side-out, an washed it with other clothes. I did not notice the problem any more, but u did not wash it many times either. i am still on the look, but the initial experience is promising.
HACK: wear the sweater with clothes of similar color. In that way, the fibers will still be there, but not visible.
Crazy idea: a lint roller might not be strong enough for the job. So you can use alternatively a vacuum cleaner to just suck-remove the loose fibers. It might be easier, it might not. I did not yet verify this solution, but it has potential.
If brushing didn't work, try the lint roller - or if feeling brave, lightly run a disposable shaver along the inside of the sweater? Just like a defuzz tool.
To prevent it occurring make sure you follow the wash care instructions. I'd recommend:
- turning inside out
- gentle wash cycle - don't overfill (maybe try handwash?)
- NO tumble dry - air dry only
- use detergent with enzymes + fabric softener