Hi Cyberqueen13
When you install a world the file gets installed to the following location
C:\Users\Your Name\My Documents\Electronic Arts\The Sims 3\InstalledWorlds
This is the location of Exotic World after you have done a install, first thing to do is check you have the Exotic World.world file in this location.
It should also contain the other worlds you have downloaded.
Also have you deleted anything in the following folder recently:-
DCCache
You can find this here:-
C:\Users\YOUR NAME\My Documents\Electronic Arts\The Sims 3
I belief this contains index file, that tells the game what is installed, you will need place the file back, you can either reinstall the world or put the file back from your recycle bin. This should allow you to select your worlds again.
To answer the question does this conflict with Awesome Mod, It's a world file, I cannot see any reason why a world file would conflict with this mod. If your having problems with that mod, you will need to speak to the designer, but I've been wrong before so I will download Awesome Mod and test the world with this mod.