You can have your own interpretation of compassion. However, if I don’t agree with your interpretation, I will let you know why.
I don’t agree with your interpretation of compassion because you claim it is unconditional, but every act is a conditional act. We do not do anything unless it will benefit us in some way, even if that is giving to charity - it will make us feel good about ourselves that we have helped somebody, it may help people like us better, it may win us good karma credits. We are the center of every enterprise. Life is about us and not others.
One of the truths that we encouraged to accept in Yoga(also in Existential psychotherapy) is aloneness. We are all actually alone. We are the witnesses of the dance of life - watching the dance like spectators, but not dancing ourselves. It is when we start to identify as the dancers that we start to develop psychological problems. As soon as we start identifying with others in the world and their needs and problems, we begin to lose our grounding and get lost.
As soon as we bring the focus of our life on our needs and problems, we regain our ground and our confidence. Therefore, put yourself before others.
We come into this world on our own and we will certainly go on our own. Even when we have no companion, we have the companion of our own self. Our own self is our constant companion. Thus learn to love the company of your own self and learn to respect your own needs and fundamental rights. If somebody is compromising your needs and fundamental rights, they are violating you and you must not put up with it. Take the most appropriate action to ensure the violations do not continue.