I am not thinking she is a gossip. It occurs to me that she is either lonely, or genuinely interested in your welfare.

I feel unsettled too when people ask about work or what I do. It is a common question to ask. It is a indication the person is sincerely interested in knowing you better. I tell them I am on stress leave. As anxiety is the biggest reason I am not working this isn't too far from the truth. On rare occasions people have pressed further. I simply tell them, "Look, I have Depression and Anxiety issues and am unable to work. Maybe one day I will return."

I have never encountered difficulty or cause for embarrassment in such situations. On the contrary, the individuals react with quite a caring attitude.