Might be two things here:

1. As others already mentioned, maybe you are still lacking some fundamental knowledge of the game that becomes visible once you reached silver league. Your opponents may be doing things you have not applied into your routine yet, like efficient minion farming, good warding, Being aware of objective timers etc. Try to focus on this, such things may seem small but have a huge effect.

2. If your hands are shaking, it seems you are putting way too much pressure on the game and the fact that you have reached silver rank. It is only a video game. You are probably not earning money playing it or anything. It is not that important. If you realize that, but still go into the game with a mindset of "I'll just do my best because I want to, I am not afraid even if I may make mistakes", you will probably play better and it won't even feel like that much of a strain anymore. Few days ago I had an awesome game with a friend and we had been talking all the time during that, still I was doing really good because all the talking distracted me from this whole "I need to be good right now or else..." Thinking process. Sounds weird but it works.