Today, I can't open iTunes and instead switches to the App Store.
If this is what you're experiencing on your iTunes, I found a solution from one of the Apple forums.
1. Tap to open iTunes.
2. And then quickly place your finger on the "Music" icon on the far left.
This will let you in to iTunes.
You will not get it the first time. Just try and catch that Music icon as if playing cat and mouse.