  We consider a class of {\em quantum Hall topological insulators}:
topologically nontrivial states with zero Chern number at finite magnetic
field, in which the counter-propagating edge states are protected by a symmetry
(spatial or spin) other than time-reversal. HgTe-type heterostructures and
graphene are among the relevant systems. We study the effect of electron
interactions on the topological properties of the system. We particularly focus
on the vicinity of the topological phase transition, marked by the crossing of
two Landau levels, where the system is a strongly interacting quantum Hall
ferromagnet. We analyse the edge properties using the formalism of the
nonlinear $\sigma$-model. We establish the symmetry requirement for the
topological protection in this interacting system: effective continuous U(1)
symmetry with respect to uniaxial isospin rotations must be preserved. If U(1)
symmetry is preserved, the topologically nontrivial phase persists; its edge is
a helical Luttinger liquid with highly tunable effective interactions. We
obtain explicit analytical expressions for the parameters of the Luttinger
liquid. However, U(1) symmetry may be broken, either spontaneously or by
U(1)-asymmetric interactions. In either case, interaction-induced transitions
occur to the respective topologically trivial phases with gapped edge charge
excitations.
