With awareness comes all possibility. To be aware means you now have the infinite number of choices laid out in front of you, but what are those choices and what is your fullest potential? To discover this you will have to play, to try to fail. So that you may grow in your knowledge and experience.
For exercising your empathy this looks like getting accustom to your surroundings feeling every thing that is around you. Learning to focus and distinguish the differences betwixt a tree, a person, or a cute fluffy cat. Each and everything has a different feel or sense to it and learning how each being feels to you will enable you to be more aware, with more awareness comes more control. Use this awareness to recognize yourself too, for you are the most important being in your world. Without you there is no world as far as you are concerned.
Learn how you feel for the times when the world becomes much to quick and all you want to do is run and hide. Know you can focus on you and you alone and the rest of the world will fade away and with a breath your world will be right once again.
Take your time and focus on yourself, see how you feel in the moment, do you have any aches or pains, how do you smell, what taste do you now have in your mouth. Then feel out to another being, how do they feel? Does their facial expression match they way they feel to you? Do you feel as if you are them? If so pull out a little and observe the feeling of them and check with yourself from time to time so you can retain that difference from them. With time and practice it will become easy to focus on all the beings around you and be free to select which ones you choose to feel. You will with ease be able to stay focus on yourself which you may be surprised to find will bring you more confidence and much greater calm.
A big reason it is so easy to get lost in the sea of others is because we are all one being here while here and now it appears we are all separated. In reality, we are multidimensional beings interwoven through space-time living here, there and everywhere all at once. This is a bit much to take in when you are first becoming aware so singling out and selecting what you feel will allow you to sail the oceans of empathy.