Ohm's law applies to electrical circuits; it states that the current through a conductor between two points is directly proportional to the potential difference (i.e. voltage drop or voltage) across the two points, and inversely proportional to the resistance between them.
It is clear that the Ohms law is applicable in case of purely resistive loads (R) or linear loads. The transformer constructed with windings on primary and secondary sides are inductive in nature which is also non-linear. Hence Ohms law is not applicable to transformers.
A transformer as whole consists of two electrically isolated circuits. And as a whole transformer doesn't follow Ohm's law because when a voltage is increased, current decreases. Ohm's law is applicable in electrical circuits i-e primary winding and secondary winding individually.