First some general advice:
A lot of players use "but my team is bad" as an excuse to cover for their own mistakes. Some of the top players can reach rank 1 in under 100 games because they know how to carry. Although HotS is a very team focused game, you will be amazed how much the skill of your own play affects your team. I'm currently rank 9 (SoloQ only) and the most effective thing I can do to get out of a rut is to stop caring about my teammates. Every time you focus on and worry about what your teammates are doing, you're not focusing on your own play. Remember that the other team has more of a chance at getting the bad teammates you complain about. If you're actually good, then that leaves 4 possible trolls/afks for your team and 5 possible trolls/afks for the other team. The matchmaking system isn't out to get you, nor is it unfair (mostly). You should be looking at improving your own play.
I don't have access to a HotS client right now, so I just have your hotslogs to work with. I noticed a few things that could be holding you back
I noticed that 70% of your games are with Zeratul, Valla and Sylvanas, and you don't have high winrates with any of them. As fun as assassins are, you should try to expand your pool. Your narrow pool is a glaring weakness to me. If you want to play mostly assassins, I would suggest adding Kael'Thas or Jaina to your pool. Both bring a lot of AoE damage and are incredibly strong right now.
Look up some talent builds. I prefer to use hotslogs to see how people in master league talent. Some of your talent choices are questionable. You should be taking Void Prison on Zeratul almost every game, but I see you only take it half the time. Void Prison is one of the best teamfighting ults in the game, you should learn to use it effectively. I see a lot of Zeratuls only use Void Prison to stop the other team from chasing down a takedown. Don't do that. If you're using it when the fight is lost, its too late. Use it to remove their key heroes from the fight. Another questionable choice is that you rarely take frost shot on Valla, despite the fact that you tend to stick to a multishot build. Her multishot build gets a huge power spike from frost shot and you're ignoring that part completely.
Pick more heroes with utility. Look at my profile on hotslogs. When I started HL, I really liked playing high damage characters like Nova and Tychus. But I know that everyone likes to do that, so I learned to play heroes with more utility. I'm careful to only pick Nova when my team needs an assassin. I played a ton of Malfurion, even before his buffs, and learned to use his ult effectively. A good Malfurion will carry a teamfight with his ult. I'm doing barely any damage, but my healing output is so high that my team stays alive and can keep doing damage. Prior to his nerf, Anub'Arak was my goto tank. I used him to dive and disrupt the other teams backline so that they couldn't do damage to my backline. It wasn't sexy, mechanically intense gameplay with lots of outplays, but it worked.