"in the right side" is a perfectly correct, grammatical phrase that can be used in written English. For example: I put my shoes in the right side of the closet.
Under the heap, Mr. Clermond lost feeling in the right side of his body.
The bag is in the right side of the driver's seat.
"My wife was trapped in the left side of house and mother in the right side".
The vein in the right side of David Cone's neck was the first indication.
Did your grandfather fight in the right side in the Second World War?
A blood vessel, I later learned, had ruptured in the right side of my brain.
There's real-time chat in the right side bar.
Awesome tool! I started using it one year ago and I never had to look for another app
Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia