How do I unblock a water pipe with rust in it?

The water content in Nepal is high in rust sometimes depending on where you live. I get water from underground so rust comes in the water and now it is blocking our shower pipe so we can't get cold water shower but for some reason we get hot water shower. I guess it is only the cold water pipe that is blocked. Is there a way to unblock it? Would liquid drano or some other caustic substance flush it out if I deposit some stuff at the joint upstairs? Or is there another mechanism like a suction that would work from the receiving side?