Yeah it looks like you're trying to implement some sort of forward converter, but it's missing a lot of necessary parts. On top of missing the freewheeling diode on the secondary, it has no means of circulating the primary magnetizing current. Also I can't see the purpose of the other secondary winding, it doesn't seem to have any useful function.
For core parameter calculation, you just want to pick a maximum flux swing in the core (200mT is a pretty safe start), then use the volt time product to go from there:
V*t=N*dB*A. Where V is the applied voltage, t is the duration of the applied voltage, N is number of turns, dB is flux swing (in tesla), and A is core area (in square meters).