Answer: No, it is not possible.
If you reflect over the x axis first, then the y axis next, then you'll perform a 180 degree rotation. The same can be said if you do a y axis reflection first, then x axis reflection next.
In order to perform a 90 degree clockwise rotation, we would need to reflect over the line y = x and y = 0 in either order. The line y = 0 is the same as the x axis.
The line y = x splits the first quadrant into two equal pieces. The angle between y = x and y = 0 is 45 degrees which doubles to 90 degrees. So we can see the relationship between the angle of rotation and the angle between the lines of reflection.