Depending on how it is ducted, the fan joining with the dryer may just be exhausting back into the room through the dryer - IOW, it may not be venting much to the outside. Also, when you run the dryer, some of that may be coming back into the room via the vent fan. So, you may not be gaining much benefit of the current actual venting.
It's also a very good idea to run the fan on a timer. It can take an hour or so, depending on the weather and the room (and how hot a shower you take) to return the moisture to static values.
Is the foundation wall poured or block? You can rent a concrete core drill and make quick, neat work of a new hole. You can use a hammer drill, make a ring of holes then beat it out with a sledge, or use a star drill (special concrete chisel) and do the same thing, but by far, the easiest and neatest is a core drill. It won't have any problems if you happen to hit rebar (if it is a poured wall), either. I like the Panasonic line of vent fans. As you've found, the bigger thing is to find one that is quiet enough that you'll want to run it. Then, make sure you run it long enough. Figure 8-10 total air exchanges per hour and run it long enough to actually help.
Note, if the shower isn't built properly, it can retain a lot of moisture, and this could add to the problem.