I read this piece of advice a couple seasons ago that I pretty much play by. Essentially, you go into ranked and play. If you lose two ranked games in a row, just stop and go do something else. Usually if I lose twice in a row, I'll stop playing ranked for the day and either go play some arams/normals or just log off and do something else. I also watched some streams of Dyrus and he was all," Even just taking 10-15 minute breaks between games can help you relax" or something like that.
Try relaxing before each game. If you constantly think about your losing streak, it'll just be a hindrance to you and already prep you to feel negative about your games. Just keep playing and if you really belong in Silver, you'll climb out eventually. When I was in Bronze/Silver I found that if I just played more and more, I eventually got better/got out. Besides that, if you keep playing, the nervousness or tense feeling you could feel from going into ranked will probably disappear and you'll just treat ranked as a normal game mode.
Hopefully you get out of that rut. Good luck.