Damp interior wall with a musky / damp smell?

When i first moved into my flat i made the huge mistake of putting the shower on the wall without tiling it (i know, it was stupid). When i realised what i had done and why the bathroom wall was becoming quite disgusting i stopped using the shower, dried the wall out as much as possible and then had a tiler come to have a look at the wall, he told me that it was dry enough to be tiled. He went ahead and did his tiling and i thought that would be that, but it isnt.

The bathroom wall is fine and i have had no problems with the tiles, however i have noticed that the other side of the wall (In my bedroom), it looks like the plaster board is damp and has started almost bubbling. This was about a year and a half ago, i have moved everything off the wall to allow air to it and for it to dry out. Which it has mostly. But now the wall looks stained and although it is not soft to the touch, if i push on it heavily i can dent it. The worst bit for me though is a very faint smell of damp in the room.

I have a baby on the way in 2 months and have started worrying about the wall and the effect on the baby so am looking for some DIY i can do here to fix the damage. I do not have the money to pull the wall down so am looking for something more suitable. Someone mentioned to me that i could put some new plaster boards over the top and paint them, while others have said that if i just paint over the wall in anti damp paint that should work because the wall is no longer getting wet.

Please could someone advise any ideas they have as i really need to get this sorted before baby gets here.

It would be handy if there were any professionals who could give me some advise also,

Thanks