what will happen if the space in this earth gets full and we have to shift elsewhere, probably another planet.

Answer 1

Which planet ? Mercury is too hot, so is Venus where you get very high temperatures when in the sunshine -and Venus rotates in less than an hour so we would be running -fast- all the time.
Jupiter is a ball of gas.
The other planets are too far away from the Sun.
You tell me : I forget Mars. Well no, I saved it for the best. There are NASA "projects" (on paper only!) to terraform Mars -Kim Stanley Robinson has been one of the project leaders-. Even if it succeeds, if we ever get there before being burnt by radiations and solar winds, what is the surface of Mars ? About the surface of India.
Not enough to save mankind!
No sir, we have to save our planet, not abuse its resources including vital space, NOT dream of another world that we could destroy later, when we are finished with poor Earth.

Answer 2

We will adapt and overcome! necessity will give rise to the needed inventions