Spikes in Inductor Current : Buck Converter
Unless you have an (expensive) current probe, it's pretty hard to make accurate measurements of inductor current. I'll assume you have a small resistor in series with the Vout end of the inductor. It's also not apparent what the switching frequency or ringing frequency is. 

If it's real, it could be ringing of the inductor at its self-resonant frequency (SRF). 

One way to deal with that is to use an inductor with a higher SRF (at least 10-20x the switching frequency. Another is to slow down the switching edges so that the energy content at the inductor SRF is low. It reduces efficiency, but it can be a good trade-off to reduce EMI. A series gate resistor is commonly used. 

Even if the noise in your output is due to other reasons, slowing the switching transitions should reduce it.