No, we are not orbiting our own black hole, Sagittarius A*. Sagittarius A* is located at the center of our galaxy, the Milky Way, but the Earth and the solar system are not in orbit around it. The Earth, along with other planets and objects in the solar system, orbits around the Sun.
However, it is true that massive objects like black holes can cause time dilation effects. Time dilation occurs due to the warping of spacetime caused by the presence of a massive object. In the vicinity of a black hole, where the gravitational field is extremely strong, time can appear to pass more slowly for an observer far away from the black hole compared to an observer close to the black hole.
If we were in close proximity to a black hole, such as Sagittarius A*, we would experience significant time dilation effects. However, the distance between us and Sagittarius A* is so vast that the gravitational effects and time dilation caused by the black hole are negligible. The gravitational influence of the black hole is much weaker at the distance of the Earth, so the effects of time dilation are not noticeable in our daily lives.