I have trombositosis. what is it and why only me in my family that have trombositosis?

Thrombocytosis: Just means elevation in the blood platelet count. It is not a genetic condition. I many cases it is reactive, which means part of a response to different problem. There is a myeloproliferative disease called essential throbocythemia, which is an illness where the patient chronically makes too many platelets.

New mutation: Essential thrombocythemia results from a new genetic mutation. I'm going to assume this is what you are describing.