It's actually not essential that you know this - if anyone needs blood, the hospital will "type and cross" for a match. If there's a massive emergency, there is a blood type that is the "universal donor" type which can be given to anyone. Hospitals give that first, if there is no time for the testing. Even if you have a card on you (say, from the Red Cross or other blood donor center where they do type your blood and put it on the card they send you), the hospital won't based a transfusion on that info alone. The risks are too great.
It's interesting to know your blood type, absolutely, especially if you have a rare type which is very desirable for donation drives. Obviously, they have to recruit more donors of the less common types. I've occasionally seen "urgent need" requests that specify a blood type that the blood banks are low on. But otherwise, it's honestly not essential.
If lab work was done on your child, including typing, it will be in the hospital records (probably buried in a ton of other info) - your pediatrician should have that. Your blood type may or may not have been done with certain lab tests your physician has ordered. Yours was probably done in the hospital when you delivered your baby because there are issues when the mother and baby are different in Rh factor ("positive" or "negative") regardless of whether one is A, B, O or AB. Your obstetrician should have that somewhere in your hospital records.
I like to know these things just because I am curious, but I have never been asked for a blood type when I took my son to the ER or when I was in a car accident and taken by ambulance to the hospital. We were asked every other conceivable question, but not that. If they need it checked, they will do it themselves at the time.