  In this work, we present independent determinations of cosmological
parameters and new constraints on $f(T)$ cosmologies, employing two new
catalogs related to HII galaxy Hubble and CMB distance priors, along with the
local standard measurements, SNIa, $H(z)$ measurements, growth rate data (RSD),
and BAO baselines. We found that the marginalised best-fit C.L. $H_0$ and
$\sigma_8$ parameters within these cosmologies can relax the current
cosmological tensions using HIIG data. This produces a larger range of
admissible values for the current Hubble constant, and when all baselines are
considered, the uncertainty bands for $H_0$ and the matter density parameter
reduce significantly.
