I still haven't figured out what the difference is between 'clothes' and 'clothing'. I know there is one, and the words each work in specific contexts ('I put on my clothes' works vs 'I put on my clothing' does not), but I have no idea how to define the difference. Please don't look it up but if you have any thoughts on the matter I welcome them.
To me, "clothing" fits better when it's abstract, bulk, or industrial, "clothes" when it's personal and specific, with grey areas where either's about as good—"I washed my clothes", "I washed my clothing", though even here I think "clothes" works a little better. Meanwhile, "clothing factory" or "clothing retailer" are perfectly natural, even if "clothes" would also be OK there.
"I put on my clothing" reads a bit like when business-jargon sneaks into everyday language, like when someone says they "utilized" something (where the situation doesn't technically call for that word, in its traditional sense). It gets the point across but seems a bit off.
... oh shit, I think I just figured out the general guideline: "clothing" feels more correct when it's a supporting part of a noun phrase, not the primary part of a subject or object. "Clothing factory" works well because "clothing" is just the kind of factory. "I put on my nicest clothes" reads better than "I put on my nicest clothing" because clothes/clothing itself is the object.
It is fascinating to me how we (or at least I) innately understand when the words fit but cannot define why they fit until someone explains it or it gets thought about for a decent period of time. Language and humans are an amazing pair.
I figure it's the same sort of thing as yards vs yardage. When you're talking about yards you're talking about some specific amount, when you're talking yardage you's talking about some unspecified amount that gets measured in yards usually.
When talking clothing you're talking about an abstract concept, when you're talking clothes you're generally talking about some fairly specific clothes. There's a lot of grey area here, e.g. a shop can either sell clothes or clothing, either works to my ear.
I wouldn't say that as an absolute statement, but in US English (at least the regional dialects I'm most familiar with), "throw on some clothes," "the clothes I'm wearing," etc. certainly sound more natural.