well, u need to check suspension components thoroughly, starting from wheel bearing, tie rod ends, dampers/springs, steering rack etc. and a good mechanic wont take more than ur 15 min on all this.
btw, wobbling occurs due to resonating components at such speeds and if you go beyond 120km/h, maybe around 160km/h u'd experience it again. and as for wheel balancing of alloy wheels, they affix weights on outer brim usually.