Mutual Induction in Transformer
So in a transformer, when an alternating current flows through the primary, thanks to the Ampere's law, a changing magnetic field is produced around it. 


A primary current flows. This induces a changing magnetic field H around it. The changing H field in the core induces a changing B field in the core.


  This induces an alternating current in the secondary. So far so good. 


No. The changing B field induces an alternating voltage in the secondary. It also induces an alternating voltage in the primary of the right magnitude to more or less cancel out the primary applied voltage. The small difference between the applied voltage and the primary induced voltage allows sufficient current to flow in the primary resistance to create enough field for this all to be in balance.

If there's a load connected to the secondary, then the secondary voltage pushes a current through the load, which of course completes its circuit through the secondary.


  Now my question is, does this induced AC not create a changing magnetic field in the secondary ...


Don't forget they are wound round the same core. Any current that flows in the secondary creates an H field that adds to the primary's H field. The phase of the secondary current is always to reduce the H field. The reduced H field generates a reduced B field in the core.


  ... which in turn induces current in the primary (just like the primary did to the secondary)? 


more or less correct. The reduced B field doesn't cancel as much of the primary input voltage, so the larger difference between the applied voltage and the primary induced voltage allows (demands) a higher primary current. The net result of the secondary current flow is to cause an increased primary current to be drawn.


  And thus, won't we have a self-sustaining circuit where the primary and the secondary took turns to induce each other?


As I said, the phase is such to reduce the field. The net result of the two-way interaction is that as the secondary supplies more power to its load, the transformer draws more power from its supply to match it.