What you're seeing in the second plot is the resonance of the output LC (500uH inductor and 16.6uF capacitor). That calculates to a corner frequency of 1.75KHz =1/(2*pi*sqrt(L*C)).
You can start by adding realistic impedances into the inductor and capacitor model. ESR of the output capacitor is important here. This should help to damp it out.
Does it need additional damping...It doesn't really matter if you are getting the loop gain performance and transient response that you desire. It will have some effect on the output impedance over frequency as well, if that is a concern.
Suggestion: When doing Bode plots...for loop gain. Set 0db in the middle of the plot on the left side. Set 0deg in the middle of the plot on the right side. Set both scales so that they have the same number of divisions. This way it is easy to quickly read off the zero-crossing, PM, and GM. The way that you have it now, it takes a lot more work. Example attached.