With respect to the Earth's direction of rotation, in the course of any single evening anything appearing to move west to east would not be a planet or star. A satellite in sub-synchronous orbit is a likely culprit however an illusion of west to east movement can be derived with reference to clouds moving in the opposite direction.
An attempt to firmly identify the object in question might be facilitated by marking its position relative to other celestial objects along with noting the time observed. Accurate time information is especially critical when using the Moon as a reference as it will move a considerable distance with respect to background stars in the course of a single evening. In addition, the Moon's position at any time amongst background stars is subject to the location of observation and can in fact determine whether or not one sees a solar eclipse. Using rising, setting and transit times or terrestrial landmarks to establish an objects identify also requires accurate information on the observer's location, time and time standard used.
In the meantime the west to east anomaly you've witnessed is obviously a UFO.