congrats on your new fixie.
that's awesome!

i strongly recommend getting either clipless or toe clipped pedals - not only for total control of your rear wheel, but it will probably be easier on your knees - you'll be able to resist against the cranks both on the up-pedal and the down-pedal (with platforms, you can only resist on the up-pedal), thus distributing the forces.

ride safe! don't forget to pedal.

Dennis