How did Andy Dufresne dig the tunnel if there was another cell next to his?

His cell was the last one on the row, so there was no cell next to his.

Edit: I should say, his cell was the last on the row and only had 1 adjacent cell to the left and he dug out a hole on the right wall.

Andy, as both a model prisoner and a cog in the warden's money laundering scheme, was given 2 priveleges; the last cell on the end of the row (a coveted cell for Andy because of its distance from most activity, which made it quieter), and a cell of his own. You may recall that he didn't set out to dig a tunnel, it just started when a chunk of the wall fell out while he was etching on it.

As a result of his 2 privileges, he was able to dig a hole in the wall that led to the sewer pipe, and he was able to do it undetected since he didn't have a cellmate.

If you watch the scene where the warden discovers the tunnel. This is an end cell. The camera goes to the window sill and now from the back of the cell, he throws the conspiracy theory along with the rocks at red and the guards their backs are to the common cell wall. And Fuzzy Brigges is hung on the main retaining wall of the prison.

Although when they first call Dufresne and the cell is shown from the first level from that angle you can't see the poster.