I've had a rough streak as well.
I made the terrible mistake of DuoQing with a friend. Both of us has it to win in Silver, and we both had a decent, 55% ish winrate on our own but if we DuoQ botlane, we usually lose the game because Top Mid and Jungle will almost always get thrashed by the enemy team, since the enemy team will have a higher MMR just because we are duoQ.
After a few games we got really tilted because we didn't know the system gives us harder games for DuoQ, so we kept losing, and we dropped a division each, with 10 more games lost than won.
We then figured out the problem and realized that we cannot carry these games since we are nowhere good enough to absolutely smash the enemy lane down bot, so we stopped DuoQ.
The problem is, the losing streak's impact lingered, since it lowered our MMR so much, I started to lose a lot more LP than winning. This made climbing up so much harder. Couple that with a bad luck streak, I kept hovering in S3, and just yesterday dropping to S4 after a 5 game loss streak.
Overall, my SoloQ winrate is a bit over 50%, with my main role, jungle, sitting at 58% playing Eve. But even if your wins and losses even out and you generally win more than lose, it really depends on the order of which the losses and wins happen. If you win 10 games in a row, then I will climb. If I lose 10 in a row I get dropped a division, and often, since I'm not a high Gold player, I don't have the skills to carry a game which is heavily stacked against me.
The thing is, especially at the start of a season, is that people's skills are highly skewed and the matchmaking system isn't smart enough to pick it up.
For example, if I get an Azir mid, who is S3 but played Azir for 15 games with 33% winrate, and his lane opponent is an S4 Zed with 30 games at a 75% winrate, its kind of obvious who wins.
I play jungler since I have the option to influence the entire map, and have a better chance of carrying, but if our midlane dies by the 3 minute mark and is 0/5 by 10 minutes, its almost impossible for me to do much.
So I'd reckon climbing early on in the season might be really hard, since a lot of high elo players (and lower) would be doing placements, or just getting back in. Some games, you would see Plat skill players against Bronze skill players in one game.
Right now its more luck than skill, unless you are a god at the game. It might get better with time though.