Because that's "Nie noszę".

These are Verbs of Motion, so they actually do show the Present Simple/Present Continuous difference.

Nope, for me „nieść” doesn't actually have 'to wear' meaning, only the related „nosić” verb – there are some dialectal differences, IIRC, so it might not be true for all Polish speakers though.

„Nie noszę koca” is how I would say 'I'm not wearing a blanket' – note through, that it is a bit theoretical, because I think „koc” can't really be worn in Polish language, we rather 'cover' ourselves with it. ;)