"I was doing my home work." puts the 'doing' in the past, but a rather indefinite past. Were you doing your homework immediately before the question was asked, as the question is being asked, or at some time much earlier? The homework is not definitely connected with the tiredness. I recommend: 'Yes, I'm very tired. I have been doing my homework.'
"I was doing my home work." puts the 'doing' in the past, but a rather indefinite past. Were you doing your homework immediately before the question was asked, as the question is being asked, or at some time much earlier? The homework is not definitely connected with the tiredness. I recommend: 'Yes, I'm very tired. I have been doing my homework.'
You could, but it is very common to use the present perfect continuous when there is present evidence (tiredness) of recent activity (doing homework). I wouldn't say that the past is wrong, but I would be more likely to use have been doing.
It doesn't seem weird to me. This may be another example of the American usage being more accepting of simple past as well as present perfect.
I was [just] doing my homework.
Or course "I was up doing my homework until 1 am" is a different story and a reasonable explanation for why you are tired.