Wow. I had very similar experience recently with my daughter Camille when she was 16 months old. She contracted a rather common bacteria after starting at daycare. (We had just started daycare, only 3 days per week, and after only 3 weeks we ended up in the ER :() At first they diagnosed it as a lung infection, and then discharged her after 5 days (and a round of IV antibiotics), but we had to go straight back to the hospital on the 6th day because of a high fever and major vomiting. They diagnosed it as a GI infection, readmitted her to the hospital, but when she woke up the next day with NO diarrhea (as expected), they started to do a series of tests to find out what was wrong, including a lumbar puncture to test for meningitis. I choked when they even mentioned the M word, but it was a good thing they did it. In sum, the bacteria got into her blood system, went to her lungs, then near her brain (the meninges). It was a bit of a medical mystery and I was exasperated at all of the "new" developments, but in the end I was fortunate that they made the right diagnosis and took her case VERY seriously. We've been doing some follow up tests with her, including blood work on all three of us to determine if there was something in her genetic makeup that makes her predisposed to this. So far, all tests are coming back normal and she is good as new. :) But its a similar story as you- she was exposed to something fairly common that hit her really hard- "went wild" as your doctor might say.
This is my advice to you- although it is so difficult to see your baby suffering in any way, chances are it is worse on you than her (seriously). She will be feeling better soon once the meds start kicking in. Given her tender age, she will probably be sleeping most of the time, but care for her as you otherwise would at home- lullabies, smiles, love. And be thankful that they have a correct diagnosis and caught it in time and can treat it aggressively, even if it means a 3-week hospital stay. Though a very serious illness, it is common enough that doctors know how to effectively treat it, and what to do for any follow up care. My daughter was a little older than your baby, so I was pretty concerned of any so-called emotional side effects, but she rallied back the moment she was out of the hospital. Babies are resilient. Lastly, of course, don't blame youself and obsess on the "what if". It doesn't help and doesn't change anything and that's not the course you took. Hang in there, and this will soon become a distant memory.