Live streaming is hugely popular at the moment, but if you have shaky hands, or you would like to share your screen with your audience then perhaps using your desktop, rather than your mobile phone may be the solution that you are looking for.
Facebook recommends a few broadcasting tools, which you can find here, however, I am a big fan of “free” and you can't get better than OBS.
OBS (Open Broadcast software) is very similar to Wirecast, but it is free. As you know, I never add a tool to my toolkit unless I have tried and tested the product myself, and this product is excellent! It is a little bit complicated to set up, but once you have it working then its easy peasy.