Both are correct. 'Look' and 'feel' can be used in either simple or continuous form to describe the current situation with no change in meaning. You look nice today = You're looking nice today. I feel sick today = I'm feeling sick today.

The factual meaning of the two sentences is exactly the same, especially in the presence of the word "today" which firmly establishes a time frame. However, it does matter which one you use because they "feel" different . They create different impressions. #1 is a simple statement of fact: "He looks upset". Saying it this way gives no hint that you have paid much attention to John. #2, instead of stating a fact, paints a _picture_ of John. "Looking upset" acts as an adjective that _describes_ John today. It is as if the speaker painted a picture of poor John looking upset and shows it to the listener. Oh my goodness! He is _looking_ upset. The present participle "looking" has the ability, as present participles always do, to convey the idea that you observed him over time. This means you paid attention to him. It means it is more likely to mean that you are concerned.

They are both correct.