Ahhh. I think I can shed some light on what happened.
Urine starts off being acidic and has very little smell. There are different explanations from different "experts" on the internet on what happens, but the end result is that that urine dries to form alkali salts that are phosfluorescent (glow in the dark) under UV light. (Which is why carpet cleaning professionals will use a black light to locate animal and human urine stains on carpets and upholstery.)
Apparantly, it's those alkaline salts that cause the smell we associate with urine, and the odor they release is dependant on the amount of moisture and humidity. The reason why dogs will repeatedly "mark their territory" in the same spots is because with each marking, the moisture from the new urine increases the amount of smell from the existing alkaline salts, and deposits the urine needed for more alkaline salts to form there.
Here: go to this web site:
http://cleanfax.com/index.asp
Cleanfax is the web site of the Cleaning & Maintenance Management Institute which is an organization established to further the goals of the cleaning and maintenance professionals.
Once there, type "black light" (without the quotes) in the red search engine on the top left of the web page
Then, in the red search results on the right, click on the article entitled "The truth about cats and dogs".
On the page you get to, you will see a red box entitled "Related Information/ What makes urine smell?". If you click on that link, you'll get the following:
“You have to understand the molecular structure of what it is we smell in order to be able to destroy it,” says John Heffron, marketing and sales manager, Thornell Corporation, Penfield, NY. “Once you diagnose what these sources are, then you can find an agent that addresses them specifically.”
Fresh urine typically has little odor. The offensive urine smell begins once it starts to decay and release ammonia gas. The second level of decay releases mercaptan (a foul-smelling organic compound), which comes from the same family of odor as skunk spray.
Natural bacteria attack the urine as it breaks down, digesting the urea, sodium chloride, lipids and phosphorus- and potassium-containing urine. The bacteria leaves behind phosphate salts, which stick to the carpet, making it extremely difficult to clean up.
Richard 'Bo' Bodo, an IICRC certified Journeyman cleaner and the Western Regional Manager for Nilodor, Bolivar, OH, notes that phosphor salts are the basis for several carpet problems.
“These salts are what release the odor, and they need heat and humidity to do that,” says Bodo. He says animals tend to urinate in the same spot, “every time adding heat and humidity to the salts already in the contaminated spot” and in turn it “releases an increasingly more pungent odor each time.”
He also notes that another problem with these is that while urine begins as an acid, the salts that remain are alkaline, and “if left unchecked they will strip the carpet of its red and blue dyes, thus leaving only the yellow dye, which looks like a urine stain and cannot be fixed unless it is re-dyed.”
end of quote
SO, I think what happened is that the strong acid you were using dissolved these highly alkaline salts left behind from the urine spilled onto the tile floor and absorbed into the grout, and it was the organic gasses released from the dissolving of those salts that made you gag.
Strange as it may sound, if you Google "urine salts", you'll find an awful lot of information about them. The reason why, of course, is because an awful lot of money is made removing pet accidents from people's carpets and upholstery by cleaning professionals, so an awful lot of money has been spent by the chemical companies to understanding them so that cleaners can be developed to remove them.