116. I am an American/Canadian, but I am Chinese/Japanese

I am American
I am an American
I am Chinese
...are all correct.

If you say: I am a Chinese it feels like the sentence is incomplete (you are a Chinese what?), you would need to say something like: I am a Chinese person. Typically nationalities that end in '-an' can be used as a noun to mean a person of that nationality (as well as an adjective), e.g. Australian, Canadian, American, German etc.

Therefore you can say things like I am an Australian, or I am an American. Other nationalities tend to only act as an adjective, e.g. Chinese, Japanese, English, Swedish etc. So sentences like 'I am an English' or 'I am a Chinese' sound incomplete because they have no noun.