Context. Investigating the magnetic field structure in the innermost regions of relativistic jets is fundamental to understanding the crucial physical processes giving rise to jet formation, as well as to their extraordinary radiation output up to γ-ray energies. Aims. We study the magnetic field structure of the quasar CTA 102 with 3 and 7 mm VLBI polarimetric observations, reaching an unprecedented resolution (∼50 μas). We also investigate the variability and physical processes occurring in the source during the observing period, which coincides with a very active state of the source over the entire electromagnetic spectrum. Methods. We perform the Faraday rotation analysis using 3 and 7 mm data and we compare the obtained rotation measure (RM) map with the polarization evolution in 7 mm VLBA images. We study the kinematics and variability at 7 mm and infer the physical parameters associated with variability. From the analysis of γ-ray and X-ray data, we compute a minimum Doppler factor value required to explain the observed high-energy emission. Results. Faraday rotation analysis shows a gradient in RM with a maximum value of ∼6 × 10⁴ rad m⁻² and intrinsic electric vector position angles (EVPAs) oriented around the centroid of the core, suggesting the presence of large-scale helical magnetic fields. Such a magnetic field structure is also visible in 7 mm images when a new superluminal component is crossing the core region. The 7 mm EVPA orientation is different when the component is exiting the core or crossing a stationary feature at ∼0.1 mas. The interaction between the superluminal component and a recollimation shock at ∼0.1 mas could have triggered the multi-wavelength flares. The variability Doppler factor associated with such an interaction is large enough to explain the high-energy emission and the remarkable optical flare occurred very close in time.