All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The Hadith referred to in the question was narrated by Abu Dawood and classified by Shaykh Al-Albani as Sahih (authentic) in Sahih Abu Dawood.
What is meant by the words of the Prophet in this Hadith (my Ummah): They are the nation of Muhammad who believed in him and believed in what he brought, and they are the Muslims and not others. There is a view that says: Rather, they are the companions in particular. Another view says: What is meant by the Ummah here is the one who followed the example of the Prophet as it should be, and complied with what Allah commanded, and refrained from what He forbade.
Allah knows best.