Nichols plot confusion
Probably no error with the math, but realize that the chart is not a grid. It looks like the chart below. So if charting by hand make sure the grid is a Log scale of the magnitude or \$20\log_{10}(|G(s)|)\$ on one axis and phase on the other. If the closed loop transfer function is given, then a nichols plot is the open loop version, so it will need to be converted from closed loop to open loop.

Source: http://courses.me.metu.edu.tr/courses/me442/handout.html