Since you are posting on a smurf account I can't really give any advice about your recent game(s) against Riven, so I'll stick to general advice.
I'd say Riven's strongest point is that she can turn pretty much any matchup into a skill matchup. However, Riven can be pretty reliant on snowballing to actually be useful in the game so if you can avoid dying and keep up in CS and experience, you should come out ahead on most champions.
I typically just pick a tank with good innate damage and the ability to farm from ranged when necessary, such as Mundo or Shyvana, and rush Sunfire Cape. You are enough of a damage threat to actually fight her if you are intelligent about trading and you are tanky enough that you may be able to survive an all-in attempt.
I find Nasus is also a decent pick against her if you know how to farm under your tower early and avoid giving her chances to all-in you, but I wouldn't recommend him if you can't reliably do that.
Irelia is a skill matchup against Riven. IIRC, it's recommended to max E against Riven and get an early Sheen if you start snowballing. That lets you chunk her with E and the sheen proc and back away before the stun wears off. I'm not sure if I would recommend maxing W first in this matchup, since Rivens' Q3 and her W can both cancel your autoattack animations.
Cho'gath is a good pick against Riven because of the silence and durability/sustain, though you do have to be careful early. You might not kill her in lane until later, but between your passive, your ultimate's health, and a Frozen Heart she won't be killing you either. In addition, your silence robs her of her damage, mobility, and shield during teamfights, so your team can easily kill her before the slience wears off.
I would avoid choosing squishy champions since they are pretty much food for a good Riven if you make a mistake.
As most champions, I would recommend starting with Cloth5 and to focus on surviving the early laning phase. Know how Riven typically plays, where and when they want to engage, and Riven's power-spikes. Also, know her cooldowns; while they may be short after she gets some levels and buys CDR, early game are a decent duration and give you opportunities to make trades in her advantage.