So, the verb "nosić" takes Accusative, and for this reason you say "Noszę koszulę", as you noticed. Feminine ending -a turns into -ę in Accusative.
However, there are several genders for which the Accusative form is identical to the Nominative one. Those are: masculine singular inanimate, neuter singular, and 'not masculine-personal plural'.
"ubrania", being plural but not 'a group with at least one man', belongs to the third category.
Basically, "Noszę ubranię" would be correct if "ubrania" was singular (feminine singular). But it's not.
Apparently in Polish they use different expressions to say "I wear" and "I am wearing" (or just wearing in general). We are used to present simple and present continuous being the same in this language, but this is one of the rare cases when that's just not it. In short: They use "nosić" for "to wear" and "mieć na sobie" for "to be wearing"(literally translated to "have on oneself") For a better, more in-depth explanation follow this link: https://www.duolingo.com/comment/27628688