A word/phrase meaning "to ask about a person's feelings"?

Solution 1:

You already found the phrase. It is ask about.

Speaker A: "Are you feeling well?"

Speaker B: This is the first time you are asking about me since morning. You're not thinking about your business anymore?

Though, if Speaker B had some kind of illness or injury, worry about can be used also.

Speaker A: "Are you feeling well?"

Speaker B: This is the first time you are worrying about me since morning. You're not thinking about your business anymore?

Solution 2:

This is sometimes referred to as giving a person consideration:

3: thoughtful and sympathetic regard
_{(Source: Merriam-Webster)}

So, I would use it like this:

This is the first time you have given me any consideration since morning.

This can be shortened into:

This is the first time you have considered me since morning.

Solution 3:

I'd describe Speaker A as being solicitous:

ADJECTIVE

1 Characterized by or showing interest or concern:

she was always solicitous about the welfare of her students

a solicitous inquiry

EXAMPLE SENTENCES

Among the most important of these is the central role of the extended family, which is extremely solicitous of the welfare and reputation of its members.

The nurses and staff who previously had been so solicitous of his welfare were overjoyed at his new appearance.

He is attentive, even solicitous, and Theresa accepts a dinner date.

(Definition and examples from oxforddictionaries.com)

Solution 4:

This is the first time you've shown you cared since morning.

The regular past participle, showed, is also a possibility

(Not sure about the "since morning" bit. I'd prefer since this morning, or since yesterday morning.)

Examples in print:

Now, if you'd gone on the cruise with your mom, that would have shown you cared

Even so, the attempt might've shown you cared, at least a little

I realized that's the way you showed you cared. By protecting the people and things you loved.”

Maybe if you showed you cared rather than just saying you do, I might start to believe you again.

Solution 5:

Here are two possibilities that came to my mind.

Speaker A: "Are you feeling well?"

Speaker B: "This is the first time you've been curious about my health since this morning. You're not thinking about your business anymore?"

or alternatively

Speaker A: "Are you feeling well?"

Speaker B: "My health hasn't concerned you since this morning. Business no longer on your mind?"