As someone else mentioned, Sivir hard counters Cait. Take fleet and just perma push her. Cait wins lane by pushing her laner into tower and then harassing them under it. If you're pushing instead, she will struggle to harass because then she has to choose between gaining gold from minions and hitting you. Furthermore, if she does it when she has a big wave stacked against her, it will do a lot of damage.
For her Q, its actually pretty easy to dodge and you do take reduced damage when it goes through minions, which most Caits if they're being pushed in will be trying to use Q to push their wave back out instead. Her traps, Q, ult, and net are all spell shield able.