I have a Master of Social Work and am an empath. I personally found it hard to be a social worker because my feelings of connection with the clients I served were intense. In my experience , being a successful social worker means learning how to make a connection with clients that includes the right level of objectivity or distance. This balance makes it better for you to ask questions and deliver services that help the client gain insight to help themselves. In addition, you don't want your feelings to overwhelm you or your clients. (If you client has to worry about making you sad, then the client can't focus on their needs.)
But have no fear!
Being an emotional person will be a benefit to you in a helping profession. The skill you need to develop is managing your feeling so they don't (a) overwhelm you or your client(s), and (b) you can be in the right place to ask insightful questions/offer resources to help the client develop the answers they need to grow.
In social work, there is something called "supervision." This is a formal process where someone more senior to you offers you regular "therapy" focused on your work/client life. The point is to help you process your feelings about and in relation to your clients so you can be a better helper to them. I remember one time when I was working with with homeless people - I felt guilty because I had a home and money in the bank. I talked with my supervisor about it and she helped me see that my role was to make sure my clients had the same privileges that I did. This supervision helped me transform my guilt into a renewed commitment to helping my clients achieve their goals of housing and financial success.