End June - Mid July is rain season in Shanghai. It's not tropical rain, so when it rains it goes on forever.
Whenever it rains, it's impossible to get a taxi or Didi (chinese uber), so your best bet is to use public transportation especially when you are in a rush.
Shanghai's subway system is very vast and advanced, wherever you want to go, you should be able to take a subway to.
You can also find venders selling umbrella near exits of the subway too.