How the ranked system works is that there are two systems.
One that you see LP(League Points), which lets you go up and down tiers(bronze, silver, etc) and divisions(B1,B2,B3,B4,B5, etc).
The other is MMR(MatchMaking Rating). This was the old rating system that is now hidden, but still important. This basically determines how much LP you gain/lose when you win/lose a game.
So since you got into B3 and shot up quickly, I'm going to assume you were gaining more LP when you won and lost less when you didn't. If you gain more LP then you lose, it usually means that your MMR is higher then whatever tier/division you are currently placed in. So you shot up pretty quickly. When you hit B1, though, you started to lose, so then you started getting placed against people who were lower then you and since you kept losing to them, you kept going down in both divisions and MMR. It could be that you went on a big win streak or a big losing streak or it could be you just finally hit your ideal rating. Since you are a new account(new to ranked at least) it should mean that you started off at a standard MMR rating, which I think is around/close to Silver. Anyways, you probably lost the first few in you placement matchs, since those are the ones that are most important to determining where you get placed in Ranked. After your placement matchs, you are supposed to have to play about 50-100 games to reach your "ideal" MMR/League and justs looking at your profile with the amount of games you've played, I feel you are close to your "ideal" spot.
As for you feeling you are getting placed with bad teammates, I feel it is because you have hit your current skill "cap" for now. You are not able to solo carry your games anymore, so you start to look to your teammates for help, since they are the ones who can bail you out. If they play badly as well, though, it just seems worse.
Anyways, while skimming through your match history, you really need to work on your CSing and probably on positioning. You seem to have a high amount of deaths in games where you are playing a carry role, which means you are probably taking more risks then you need to. Oh and UPGRADE YOUR TRINKET. You can do this in ranked, but for me I like to do my "training" in team builder or blind pick. This way you can get the experience of playing better without sacrificing your MMR/League if you lose. You can also take more risks and experiment more without having to worry about losing. Also if there are champions with spell combo's/rotations that you want to try out, go play URF while the mode is still up. You can spam them and get practice a LOT faster then if you did it in a normal game.
Hope this helps.
