There are very basic two mistakes in the first sentence:
One mistake is the verb form. If you are describing a picture, you need to say 'The boy is wearing jeans and a shirt'. This is the present continuous, used to describe what he is 'doing' at the moment. Yes, I know that 'wearing' something isn't exactly an activity, but you still have to use a present continuous. The present simple - wears - would be used for a general fact or a repeated activity, for example, 'He always wears jeans at the weekends'.
The other mistake is the lack of article before 'shirt'. 'Shirt' is a singular countable noun, so it needs an article or another determiner before it.
'He has jeans and a shirt on' is fine.
If your teacher makes many more elementary errors like this, you may want to think about getting a new teacher!