This morning an HR person asked my boss if I was drinking this morning.
I went home sick after an hour at work. I did not drink this morning and
did not drink at work. Can some action be taken against me because she
thought I was drinking?

So what did your boss say? Is there a particular reason why the HR person might think that?

And to answer your question, no, you don't get to take legal action because of what someone thought.

I think she asked my boss that because I went home sick. I did
drink last night during the football game and that might be why
I went home sick. I didn't think it was their business why I was
sick. I didn't smell like alcohol. I shower every day and am a clean
person.

I believe you. But it still does not give you legal recourse. She is entitled to ask the question if she thinks you were drinking, even if she is wrong.

Do you really want a law that allows you to sue for asking a question? Someday you might ask a question that someone doesn't like.