Jessvet, Yes it would hurt me. I agree with both Rene and karma. I would like to talk about being an empath but I feel people, at least the people I know, would not be open minded to listen and understand. That is what is so wonderful about being in this group, a place to talk and share.
I cannot really answer tat question, as I would not tell anyone to not tell anyone (anymore). Maybe I had learned to stand up for who and what I am, when I came out as gay (years before my spiritual coming out) . Realizing that I am an empath was just another facet of my being that I became aware of. That said it took me years to be firm in my diagnosis that I am an empath. Being an empath goes against so many other spiritual teachings - which usually tell you that you have to take responsibility for all your emotions, and that they are all self-generated. As such I observed my feelings and thoughts for years, before I was firm in my diagnosis of being clairsentient (the term empath I only found later on). It is all in a book now I have written too, so there is no way to 'hide' it anymore.
So I do not know your life circumstances, there might be reasons why you do not want to be 'open' about your abilities (heck, I would not run around screaming I am gay in a homophobe country either), but it does sometimes also pay to have a closer look at the reasons why we do not openly admit to all facets of our being - and get rid of any unnecessary potential shame...
Love and Light!