Do I need to replace the wall after a shower head leak?

So I was going to replace my shower head, but it was on there pretty good and started twisting the shower arm. I twisted the shower arm back into place maybe too tight and tested the water and didn't see any leaking.

I was going to buy a new shower arm the next day and install, but I never told my wife to not use the shower so the next day while she showered it broke at the threads in the wall. She turned off the water called me, but it was to late. The downstairs ceiling already had water damage because it came down through the two water pipe holes in the wood above.

I cut out a piece of the drywall ceiling so I could make sure the leaked stopped and dry it out. Now I'm wondering if I need to replace the wall between the shower and bathtub because mildew, etc. The walls on the outside don't show signs of water damage.

Would the water that sprayed out just fall below and I shouldn't have to worry about the wall between the shower and tub? Are the walls usually something other then normal drywall on both sides? I used a fan to blow air into the shower arm hole. Does anyone know if that would be enough or I need to rip apart the wall?

Thanks.