Do I need to remove this enclosed shower and check for mold?
First go to a home store and look at how this style tub and shower surround are built. 
Next realize the tub has a lip that extends up and the bulge at the base of the surround is to overlap the lip on the tub. 

If you want to purchase a new surround try removing it, 
You have probably shot some water up inside the wall and that can cause mold. 

If you want to keep mold from becoming a problem seal the joint with a latex calking or any silicone bathroom calking with mold inhibitors. 

Whatever you do don’t pull the drain and see all the gunk hair and? in the drain or you may want to move out. 

Seal the joint and forget about it would be my advice.