But as I started, I couldn't stop dying.
If you die once to your lane opponent they get a pretty solid advantage.
Die 3 times in 10 minutes and you probably lost the game for your team.
Anyways - the first death is the most important one for talking about balance purposes. The 2nd, 3rd, and especially 4th kill in a row are not equal - as any champion that's snowballing is going to have a considerably easier time getting more kills: especially against opponents starved of gold and XP.
Also - dying 3 times in lane is actually fairly easy to prevent. You just have to transition to playing smarter rather than harder, respecting your opponents power and probably giving up some CS, holding off on a repeat confrontation until you get an edge while you go into survival mode.
I'm getting the overwhelming sense what you did was try to 1v1 Riven during one of her noteworthy power spikes very early in the game, and then proceeded to duel her over and over again to defend your honor while she just snowballed harder and harder, to the point coming within 1 screen length of her meant death by the time you tryed evading fights with her.
Under that scenario any champion is going to kill you over and over again. I've even hit point-of-no-return snowballs on supports like Sona and Leona.