I really like reading your poetry! Your phrasing is so unique and creative.

Your sentence: "People are in a rush", is 100% gramatically correct. However, here are some corrections: 

My Rain Shoe

I walked here, there,
And everywhere

Even to the big blue
And to the green hill

Rain is all over
Like a melody lasting forever

People are in a rush
Opening colorful umbrella (what do you mean here?)

Only me
Slowly walking

As hiding inside my rain shoe (again, what is your meaning ><?)
There's no cold or fear to hold. (do you mean inside?)


END
(need a help to change "in a rush" into a better expression way)