Not worried enough

Two weeks ago my 7 months old daughter (first baby) started to have a very high temperature (around 40 C). We followed all the instructions on the state medical webpage. She did not have any symptoms besides high temperature, but we read that it could be the case for small babies and that is all right in case it does not exceeds 3 days.

I tried to stay conscious and not to be overly worried.

On the forth day we went to the doctor. She inspected my daughter and reassured that everything was normal. The doctor said that there was no need to do a blood test for now and told us to wait 4 more days, most likely our daughter would feel good by then otherwise we should contact medical authorities again.

On the next day in the evening the temperature was continuously high and it looked like our baby started to loose her mind (we lost eye contact with her and she was acting very strange). My husband and I made a decision to go to the hospital in 30 min in case it does not change and our baby does not eat (I am breast feeding) or go to the toilet (supposedly good signs in accordance to the doctors). Fortunately she did eat and I was up all night taking care of her (she was waking up every hour because of the high temperature). Sometimes we gave her medicine to treat fever, but not so much because we believe that it is important that her body fights the cause of fever in the first place.
So the next day we decided to go to the hospital and not wait any longer like we were advised.
The new doctor immediately took blood test and it appeared that our baby had an infection that can only be treated with antibiotics.

We went through a lot of pain but it seems like everything is good now.

Last week I was talking with someone and she mentioned how dangerous it was for our baby to be with such a high temperature, how wrong that other doctor was and that the baby could even have died.

It made me think again about all the situation and wonder if I should have actually been more worried. Although we talk a lot about how worry is not necessary, now it seems to me that I should have done more, should have contacted more doctors etc. I know this blame is not serving me now and I did learn my lesson for the future but I can’t even imagine talking to someone for whom it did not turn out as well as for us in the very end and the baby died although it could have been prevented.

Help me here please. Where do I make an error if so?