Hi Evan
Yes, you have a very serious situation at hand.
The label clearly states the product was intended for fiberglass surfaces, and damage could occur to porcelain. I have seen way too much damage done to ceramic and stone surfaces because the end user didn't read and follow manufacturers instructions. This occurs with cleaning services, home owners, and professionals alike.
Do you have any extra tiles on hand? What is their finish (glossy, honed)?
If so, I would treat them with "The Works" to try to duplicate the issue you have in your shower.
If that's not possible, these are the two routes that I suggest.
1. I've had very good success with "antiquing brushes" on etched porcelain. This method should only be performed by professionals. I also suggest TESTing to determine results.
2. The second method is more is more of a "band aid" treatment. Instead of wax, I suggest doing a TEST area with Aqua Mix Enrich 'n Seal. Again, if this could be Tested on a sample tile vs. your shower would be ideal. It is critical to follow label instructions which include that the surface in totally dry, and all excess material is buffed off.