Your letter is baffling. Assuming it’s for real, I’m sorry – well, not really – to have to tell you that Mrs. A had the right idea. And yes, we do stand in contrast to non-Jews who are not committed to Toras Moshe and thereby have no obligation to heed its laws.
You say you could have “died in a sea of blood” and that Mrs. A had no business “cutting you off from the information you needed.” Sounds like Mrs. A sized up the situation and determined that a “need for information” does not warrant desecrating the Shabbos, particularly under her roof.
On the other hand, it is somewhat surprising that an “extremely competent nurse” (who you indicate knew quite a bit about the condition) could have seen no other way to calm your fears than to indulge your compulsion to surf the Net on Shabbos. Perhaps she was simply uninformed in Torah law or had allowed her compassion to get the better of her.
You seem to have been well enough to browse the web through “cup after cup of tea.” That being the case, there was obviously no compelling reason for you to be mechalel Shabbos, and you could have easily waited until after Shabbos to either seek a medical opinion or do your research by the technological means at your disposal.
My own web research (on this weekday) informs me that Hematuria is not necessarily an indicator of anything more serious than a urinary tract infection. Hopefully you’ve since been evaluated by a competent medic and are on the mend.