I wish pro vods were searchable via champ.
The thing with Sivir is that post critochet rework, she scales well into late game. She's the best adc at clearing waves, even under tower, so she can survive really any laning matchup she gets, and can even work with a roaming support. At my high silver-low gold elo, the only champ I care about against her is Cait, and I'll pick Cait happily into her, since that range difference is so brutal I don't even care about missing the ult. Ashe would be a problem too, except more of her power is put in her ult, and it's so easy to shield.
But the point of Sivir is midgame. Just survive until then with your team close in gold and use your ult for picks/favorable engages. Because of how much of her power is in her ult, I think more important than what champs you play against is what champs you play with. Voli, Singed, Udyr, Ali, Olaf, Garen, etc.--these guys engage so hard with that speed boost.
As long as you have an IE and an ER in your inventory by late game and pick your engages well, you'll be fine. Critochet for all the damage!